Hyperbola Definition and 107 Threads

Homework Statement Integrate between y=0 and y=-0.5: ∫((y+0.5)/(0.5-y)) dy Homework Equations Can you please show me how to integrate it...Then I will be able to take it from there and substitute in the appropriate values. The Attempt at a Solution Quotient rule in...

I've got a nifty java program done which calculates the orbit of a body around a gravity source. The math and physics are all done for a body around a single gravity source and how to figure whether it's an ellipse, parabola, hyperbola or straight line. But now I've got a new problem. If...

Simple question. Is what we now call a 'rectangular hyperbola' what was once called the hyperbola of Apollonius? Thanks

y=mx+-sqrt(a2m2-b2) (which is quadratic equation) So there should two tangents from a point but if we draw then we can even draw four tangents. example; consider the hyperbola x2/16-y2/4=1 from point (2,0) i think four tangents can be drawn one to right side lobe and one two left one.. So...

I found multiple sources that describe the hyperbola of a sonic boom as "A sonic boom shock wave has the shape of a cone, and it intersects the ground in part of a hyperbola. It hits every point on this curve at the same time, so that people in different places along the curve on the ground hear...

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the general equation for rectangular hyperbola with vertical and horizontal asymptotes is given as : (x-h)(y-k)= some constant Is the following also an equation of rectangular hyperbola (x-h)^4(y-k)=some constant ? I am trying to find the shape of this curve,is it similar to that of...

Homework Statement If a graph has an asymptote, does that mean it's always going to be a hyperbola? Homework Equations The Attempt at a Solution Well, I started to think of y=tan(x) and y=cot(x). I believe they would be called trigonometric circular functions as they repeat, but...

Consider the hyperbola y^2-x^2=1 (y>0) a.) Find a parameterization for the curve and write it in vector form, R(t) (b) Calculate the unit tangent vector as a function of the parameter. (c) Calculate the unit normal vector and the curvature vector as a function of the parameter.

Homework Statement An ellipse is a set of all points from two points called a focus (together a foci) has the sum of 2a |d1 + d2| = 2a A hyperbola is the same except it is difference. Now my question is, just who came up with these definitions that it must equal to 2a?? Because if I...

Homework Statement I`ll try to make this as orderly as possible, but I've got so many questions about it 1. The most "general" form of a hyperbola are \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \frac{y^2}{b^2}- \frac{x^2}{a^2}= 1 Now my question is, the first one opens with the...

Homework Statement Prove the equation(s) for the asymptotes of a standard hyperbola. That is, prove that the asymptotes for the hyperbola x^2/a^2 - y^2/b^2 = 1 are y = -(b/a)x and y = (b/a)x where foci are at (c,0) and (-c,0); vertices are at (a,0) and (-a,0); difference in distances...

Two amateur meteorologist, living 4km apart (4000m), see a storm approaching. The one farthest from the storm hears a loud clap of thunder 9 sec after the one nearest. Assuming the speed of sound is 340m/sec, determine an equation that models possible locations for the storm at that time...

Find an equation for the hyperbola that satisfies the given conditions. Foci (0, ±7), length of transverse axis 7. I am a little confused on how to solve this. I tried to solve it and I've found that c^2= 49 so I know that a^2 and b^2 must add up to 49 but I am not sure what my next step is...

Find the vertices, foci, and asymptotes of the hyperbola. x^2 − 7y^2 = 8 When I tried to solve this i got + or - 2 sqrt 2 for the vertices, + or - sqrt 64/7,0 as the focus and + or minus sqrt 65/7 divided by 2 sqrt 2x as the asymptotes. is this correct?

As far as I know, a hyperbola has the equation So how does this (below) work? Thanks!

Homework Statement P(cp , c/q) and Q(cq , c/q) are two points on the curve xy=c2. Prove that the chord PQ has an equation pqy+x=c(p+q). A variable chord of the hyperbola xy=c2 subtends a right angle at the fixed point (a,0). Show that the midpoint of the chord lies on the curve...

Homework Statement We want to create a map from (x,y) to (u,v) such that the right side (positive x) of the hyperbola x^2 - y^2 = 1 is mapped onto the line v = 0 AND all the points to the left of that hyperbola are mapped to above the line. The mapping should be one-to-one and conformal...

What is the condition for a hyperbola and an ellipse to intersect orthogonally? I have a formula for orthogonal circles -> 2g1g2 + 2f1f2 - c1c2 = 0

Homework Statement In the attached figure, which one is a chord of the hyperbola? is it AB or PQ? I am confused between both. If AB passes through the focus perpendicular to the axis, it is called latus rectum which is a focal chord. But in some figures I saw PQ as a chord. Please...

Homework Statement A triangle is inscribed in a rectangular hyperbola such that the tangent at one of the vertices is perpendicular to the opposite side. Prove that the triangle is right angled. Homework Equations The Attempt at a Solution I am unable to draw a valid figure for...

1)In a hyperbola, x^2/a^2-y^2/b^2=1(standard form), b^2=a^2(e^2-1) This is in the case where b is greater than a. But if a is greater than b? Will that hold good correctly? 2)If you consider the conjugate hyperbola(of the standard form),what will be equation relating a,b and e? Will it...

Homework Statement Rotate the axis to eliminate the xy-term. Sketch the graph of the equation showing both sets of axis. xy-2y-4x=0Homework Equations \cot2\theta=\frac{A-C}{B} x=x'\cos\theta-y'\sin\theta y=x'\sin\theta+y'\cos\theta The Attempt at a Solution xy-2y-4x=0 First I find the angle...

Homework Statement Find an equation of the hyperbola with it's center at the origin. Foci:(8,0),(-8,0) Asymptotes: y=4x, y=-4x Homework Equations Equation for the asymptotes of a hyperbola with a horizontal transverse axis y=k\pm\frac{b}{a}(x-h) Equation for a hyperbola centered at (0,0) and...

Homework Statement 6x2 + 8y2 + 32y - 16 = 0 Homework Equations The Attempt at a Solution I think I made a mistake. This is how far I got 4(x-4)^+3(y+9)^=120 I made a mistake. Can someone delete this thread? What did I do wrong?

Homework Statement ( URL of image in case it doesn't display : http://imgur.com/wrzYH.png ) The axes x and y are measured in miles. In the figure, the LORAN stations at A and B are 520 mi apart, and the ship at P receives station A's signal 2,640 microseconds (ms) before it receives the...

Okay, before I start: I'm sorry for what is probably going to be an absurdly easy question and I'm probably going to seem like a complete moron to everyone here, however the way I see it the only way I'll learn is by asking questions (and that's just what I've did ever since I could speak)...

Homework Statement Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the hyperbola y2−x2=4 and the lines y=0, x=3 and x=5 about the y− axis. Homework Equations Nothing specific...general equations The Attempt at a Solution So I would...

Homework Statement Find an equation of a hyperbola that passes through origin and has asymptotes y = 2x+1 and y= -2x+3 Homework Equations The Attempt at a Solution I have got the center ( 1/2,2 ) and as it passes through the center i have this equation 4/a2 - 1/(4b2) from...

Homework Statement Problem : Find an equation and sketch in x-y coordinates for the Hyperbola with vertex (-1,7) and asymptotes y-5=+- (x+1) The Attempt at a Solution To find the equation of the hyperbola i have to find the length of a ( distance from center to vertex in focal axis...

Homework Statement Draw a clearly labelled “Minkowski spacetime” diagram illustrating two events ((1) a farmer firing his laser gun at his cow, which is sitting along his positive x-direction, and (2) the cow dying) as observed by two observers (S at rest in the farmer’s and cow’s frame...

Homework Statement Find the area enclosed by the hyperbola: 25x^2-4y^2=100 and the line x=3 using the green's theorem Homework Equations Green's theorem: \int_C[Pdx+Qdy]=\int\int(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y})dxdy The Attempt at a Solution We can...

The Basis of this question is that: * Rockets launched at an angle follow the path of a rectangular hyperbola when thrust greater than their mass is produced. * That rockets fall in the path of a parabola when thrust is no longer produced, this only applies when the rocket has both x and y...

Homework Statement The hyperbola y = 1/x in the first quadrant can be given the parametric definition (x, y) = (t, 1/t), t>0. Find the corresponding parametric form of its evolute, and sketch both curves in the region 0<x<10, 0<y<10 Homework Equations Curvature formula...

Homework Statement http://img11.imageshack.us/img11/6340/conicshyperbola1.jpg Homework Equations d^2=(x_2-x_1)^2+(y_2-y_1)^2 y-y_1=m(x-x_1) m_1m_2=-1 The Attempt at a Solution I was able to answer (i) but for (ii) I would go about it like this: Find the equation of the line...

Hello. I am having some trouble with the following problem and would be thankful if any of you could help me out. Homework Statement Let C be the hyperbola formed by intersecting the cone x^2+y^2=z^2, z>0 with the plane x+y+z=1, and let \textbf{f}(x,y,z)=<0,0,1/z^2>. I am trying...

1) Find the point on the hyperbola xy=8 closest to (3,0). I honestly, have no idea what to do. I seriously do not remember discussing anything like this in class, nor having any previous problems in homework. If anyone can give me a start or walkthrough, that would be fantastic!

Homework Statement Find an equation of the hyperbola that passes through the points (-3,-2) and (4, sqrt(5)) Homework Equations x^2/a^2 -y^2/b^2=1 or y^2/a^2 - x^2/b^2 = 1 The Attempt at a Solution To solve this problem I first started by setting up two equations containing the...

Homework Statement Write the equatin of the hyperbola whose center is at the origin and has a vertical transverse axis. Homework Equations The equations of the asymptotes are 6x+2y=0 and 6x-2y=0 The Attempt at a Solution I am good at following an example (am an adult who is...

Homework Statement What is an equation for the hyperbola with vertices (3,0) and (-3,0) and asymptote y=7/3x? Homework Equations The Attempt at a Solution I solved this problem but still have a question. The answer is 49x^2-49y^2=441 (I solved it by graphing). However, my...

Homework Statement The curve y^2-3xy+2x^2=4 is a hyperbola with axes rotated from the standard position. Use Newton's Method to find the positive x-value to four decimal places for the point on the hyperbola where y=1. Homework Equations Newton's Method The Attempt at a Solution...

Homework Statement Use the discriminant to determine if the following are equations of an ellipse, parabola or hyperbola 6x^2-12xy+6y^2-5x+9=0 5xy-4y^2+8x-3y+20=0 x^2-9xy+5y^2-2=0 10x^2-9xy+5y^2-2=0 2y^2-10x+9y-8=0 Homework Equations The Attempt at a Solution I got these...

Hi, I am graphing a hyperbola and have completed everything, except I am not to sure how to draw the final curve in. I have the center, foci, vertices, and axis'. I cannot seem to find any information on actually plotting the curve in. Am I supposed to freehand it in from the vertice and follow...

http://img184.imageshack.us/img184/6506/hmmyh4.jpg The question ebfore had me find the equation of the tangent for any parametizaton values of (x(t),y(t)). Which is y = -x/t^2 + x(t)/t^2 + y(t) I'm pretty sure the case that a tangent to the hyperbola can't pass through the point is...

Homework Statement The normal to the hyperbola (x^2)/2 - y^2 = 1 at P (sqrt 3, sqrt 0.5) cuts the y-axis at A and the x-axis at B. Show that PA:PB = 2:1 Homework Equations Equation of normal to general hyperbola at (x1,y1) is x(a^2)/x1 + y(b^2)/y1 = a^2 + b^2 The Attempt at a Solution...

Does the plane that intersects the cone need to be parallell to the axis of the cone to make the section a hyperbola, or is it enough that it is not parallell to a generator? If the latter is correct, can one say that a parabola is a special case of a hyperbola?

If you partially differentiate the equation of a hyperbola w.r.t. x or y do you get the equation of its asymptotes? I know that if you do partially differentiate it, the two lines that you get, intersect at its center. This is true for any conic and pair of straight lines. What about other...

Sorry to be constantly asking for help. But I think this will be the last in a while. During my math's class, I asked my teacher why the hyperbola was named liked that. She didn't answer me and ordered me to make a presentation about it. I have done some research work but I would like to make...

Using a domain of {x | -50 < x < 50} and a range of {y | 0 < y < 20}, determine the following types of equations that you could use to model the curved arch. The equation of a hyperbola in the form , where b = 10. The lower arm of the hyperbola would represent the arch...

Your task is to design a curved arch similar to the a tunnel for cars. with a horizontal span of 100 m and a maximum height of 20 m. Using a domain of {x:-50<=x<=50} and {y:0<=y<=20} determine the following types of equations that could be used to model the curved arch. the equation of a...