Conics Definition and 59 Threads

Hello: I'm not sure if there's an accepted canonical form for a quadratic equation in two (or more) variables: $$ax^2+by^2+cxy+dx+ey+f=0$$ Is it the following form? (using the orthogonal matrix Q that diagonalizes the quadratic part): $$ w^TDw+[d \ \ e]w+f=0$$ $$w^TDw+Lw+f=0$$ where $$...

The text says that the following conic, r = 15/[3-2cos(theta)], can be rearranged to 5/[1-(2/3)cos(theta)]. The graph of the conic is an ellipse with e=2/3. Then it says that the vertices lie at (15,0) and (3,pi). How did they find the vertices? Thanks.

Homework Statement Identify the following figures in the plane, saying if they are circles, ellipses, hyperboles or parabolas and giving their centers, rays, foci, and guidelines as the case may be:Homework Equations x² + y² - 3x = 0 The Attempt at a Solution x² + y² - 3x = 0 x(x - 3) + y² = 0...

Hi, the problem is parametric families: To find Differential equation of all the conics in the plane with the origin in the center But when you speak of center at the origin being the equation of the conics: Ax ^ 2 + Bxy + cy ^ 2 + Dx + ey + F, is it correct to take the origin by making x and...

It is said that curves of the second order which we usually refer to as ellipse, parabola and hyperbola, i. e. conics, are all represented on projective plane by closed curves (oval curve), which means there is no distinction between them. Why is it? Projective space can, in principle, be...

Homework Statement Hello! I am repeating conics, and have stumbled upon this paragraph on purplemath.com " Then a = –1/9. With a being the leading coefficient from the regular quadratic equation y = ax^2 + bx + c, I also know that the value of 1/a is the same as the value of 4p, so 1/(–1/9) =...

In my study I deal with tubulars frequently, and it is well known how to calculate stresses due to external pressure on a (hollow) uniformly-thick cylinder (i.e. a pipe). Suppose now that I have a cone, tapering downward like a V, with a hollow cylindrical interior (like the inside of a pipe)...

Homework Statement if the tangent at a point P("theta") on the ellipse 16 (x^2) + 11 (y^2) = 256 is also tangent to the circle (x^2) + (y^2) + 2(x) = 15 then ("theta") = ?? 2. The attempt at a solution {{{{ i have taken "theta" as "d" }}}} P [4 cos d , (16/(sqrt11)) sin d] equation of...

Hi. I am given the following problem. A small bridge is shaped like a semi-ellipse. Given that its maximum height is 3m and that its foci are located 4m from the centre find the height of the bridge at a distance of 2m from its edge. So the problem give me the values b= 3 and c=4. With this we...

When a object of mass non insignificant is traveling in space and is sob influence of one gravitational field, the trajectory described by this object is a conics (Ax²+Bxy+Cy²+Dx+Ey+F=0), but and if the object is sob influence of two gravitational fields, so the equation the described this...

Find equation for center at (1,2) and vertex at (1,8) and Minor axis length of 4?

Homework Statement Hi wondering what the directrix is for this Homework Equations r = (20)/ (2+sin(theta)) The Attempt at a Solution I factored denominator so it read 2(1+ (1/2)sin(theta)) ...So I said e times d = (2/20) and I got d = (1/5) because e is (1/2). Doesn't make...

What is the most motivating way to introduce the sketching of conics which have a cross product terms? This topic involves a lot of other stuff such as eigenvalues, orthogonal matrices, completing the square etc. I find a significant number of students get lost in this forest of sketching...

What is the most motivating way to introduce the sketching of conics which have a cross product terms? This topic involves a lot of other stuff such as eigenvalues, orthogonal matrices, completing the square etc. I find a significant number of students get lost in this forest of sketching...

What are the real life applications of quadratic forms? I have used them to sketch conics but are there any other applications?

What are the real life applications of quadratic forms? I have used them to sketch conics but are there any other applications?

Homework Statement The equation ##x^2y^2-2xy^2-3y^2-4x^2y+8xy+12y=0## represents?? Homework Equations circle: ##x^2 +y^2 = a^2## The Attempt at a Solution i know this has something to do with seperating out the variables but i don't seem to get the req equation

Homework Statement Through a given point in the plane of an ellipse prove that exactly two conics (one eliipse and the other hyperbola) confocal with the given ellipse can be drawn. Homework Equations The Attempt at a Solution Let the equation of given ellipse be...

Homework Statement Given the vector (6,-15) and foci (6,10) (6,-14), Find the equation of the conic.Homework Equations Vector = <6,-15> (x-h)2/a2 + (y-k)2/b2 = 1 Foci (h+c,k) and (h-c,k) vertices (h+a,k), (h-a,k) The Attempt at a Solution k = 6 h=-2 a=-12 I'm not sure what I'm doing. How do...

Homework Statement Find an equation is standard form for the conic that satisfies the given condition. Parabola: vertex (2,3), vertical axis passing through (1,5) Homework Equations vertex= (h,k) The Attempt at a Solution I know how to solve a problem like this if I was given the...

Hi, I've got a problem here, that I'd like to discuss before trying to implement any sort of solution. Basically I've got a planetarium simulation, in which I'd like to plot a patched conic trajectory ahead of a spacecraft . The planetarium only simulates two-body gravity, and switches...

Homework Statement Find an equation of a hyperbola such that for any point (x,y) on the hyperbola, the difference between its distances from the points (2,2) and (10,2) is 6. Homework Equations -None- The Attempt at a Solution I tried graphing it and making the (10,2) and (2,2)...

TI-84 HELP! The formulas under the CONICS app keeps converting into trig... It saying a circle is x=rcos(T) + H instead of (x-h)^2 + (y-k)^2 = r^2 How do I get the 'normal' formulas back? PLEASE HELP!

This is from my History of Mathematics course. Well, I centered the hyperbola at the origin and found the derivative. It gives me the slope of the tangent line at whatever point I want. How do I prove this?

So I've been wondering for a long time: How are conics studied in Calculus and Analytic Geometry? Also, how are they applied in real-life situations, whether it's something as simple as construction, or something as complex as physics and engineering. Ever since I studied conics in my...

Homework Statement Given the ellipse is centered at the origin and the information, find an equation of the ellipse. 1) An ellipse with focus (\sqrt{5},0), directrix; x = \frac{9}{\sqrt{5}} 2) An ellipse with an eccentricity of 4/5 The Attempt at a Solution I have to leave...

Unfortunately my inferior Canadian education skips out at least a year of math topics in comparison with my American counterparts, so conics weren't a "huge" part of our curriculum. Can someone tell me what course demands existing firm knowledge of properties of parabolas (directix, focus...

I am unable to comprehend the proof for tangent line to conics. Here is the proof as per the book (Multiview Geometry by Hartley and Zisserman). Everything is in homogeneous coordinates. The line l = Cx passes through x, since lT x = xT Cx = 0. If l has one-point contact with the conic...

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...

for this problem, I've been given the vertices of the hyperbola as (4, pi/2) and (-1, 3pi/2). the question asks to find the polar equation of this hyperbola. so what i did was do a quick sketch of the graph. (4, pi/2) is essentially (0,4) and (-1, 3pi/2) is essentially (0,1). the midpoint of...

Homework Statement There are 2 problems a and b. I've solved for both already. I just need to know how to describe them by type and orientation. In other words, what does what I got tell me in regards to type and orientation and how do I know this for future problems? (e.g. hyperbola or...

Homework Statement How do you know whether you restrict the domain or range with a horizontal ellipse ? Homework Equations x^2/49 +y^2/10=1 The Attempt at a Solution

Homework Statement graph the following: Homework Equations x^2-4y^2+2x+8y-7=0 The Attempt at a Solution So far I've gotten to (x+1)^2 = -4(y-2) If that's right, I have p = -1 and v = (-1 , 2) and directrix: y=2. Could someone double check me to see if I'm doing it right? Thanks

Homework Statement graph the following Homework Equations 9x^2+4y^2+36x-8y+4=0 The Attempt at a Solution I think I need to get it into \frac{(x-x0)^2}{a^2}+\frac{(y-y0)^2}{b^2} but I'm not sure. I have \frac{9x^2}{-4}-8x+y^2-2y=1 and now I'm stuck

Homework Statement Graph the following. Include center, verticies, foci, asymptote, and directrix as appropriate. Homework Equations x^2 + 8y - 2x = 7 The Attempt at a Solution So far I have: V = (1, -7/8) P = -2 X = -1 I have no clue where to go from here, or if I'm...

i have made a program that takes input of Ax^2+By^2+Cxy+Dx+Ey+F=0 it determines the type pf curve and finds all the related elements...now i want to ad the GRAPHS as well...but i can't find a way...i just completed my 12th standard so i don't have enough knowlege...even i can't find related...

Homework Statement http://img93.imageshack.us/img93/6889/arch4gh8.jpg [/URL] Homework Equations Above The Attempt at a Solution All good?

Homework Statement http://img125.imageshack.us/img125/6893/arch5tq8.jpg [/URL] Homework Equations On work The Attempt at a Solution Just need someone to check my work.

Homework Statement http://img103.imageshack.us/img103/3784/arch3tf0.jpg [/URL] Homework Equations On picture above The Attempt at a Solution Again, I just want someone to check my work.

Homework Statement This is the second page. http://img116.imageshack.us/img116/7519/arch2iq9.jpg [/URL] Homework Equations Formulas on picture above. The Attempt at a Solution I'am just wondering if everything looks fine.

Conics! Help Please! okay i think i have solved this correctly...still a little unsure though... y=x^2-6x+3----find x intercept first i used complete the square---- y-3=(x-3)^2 then i solved for x---- 3+(y-3)^(1/2)=x then i plugged 0 in for y and got 3+(3^(1/2)) and 3-(3^(1/2)) is that...

Were on the conic section. I need help how to choose the right interval to evaluate the arc lengh. x=5cost-cos5t and y=5sint-sin5t . I don't get how to choose the inverval to evaluate this, can someone pleasse tell me how. I just don't grasp this.

during my study on conics , I found a formula in the book regarding the classification of figure from the general equation of conics ax2+2hxy+by2+2gx+2fy+c=0 it was given that \Delta=abc+2fgh-af^{2}-{bg}^{2}-{ch}^{2} if \Delta \neq 0 then if h^{2}=ab...parabola h^{2}<ab...ellipse...

Hi, I have this homework question and I completed and found the the foci and the center for the ellipse, but I don't understand how to find the semi major and minor axis. Graph and give the center, semi major and semi minor axis and foci of the ellipse 25x^2 + 350x + 9y^2 - 54y +1081 =...

. ...|...B . ...| . ...| . ...| ----|---------D . ...|A . ...| . ...| . ...|...C Remember its a parabola connect the dots. This is what i have done x^2/a^2 - y^2/b^2 = 1 then i substituted a as 0 and b as 16 and it got me nowhere I'm guessing it has to be located at 0 but i...

Hello, I started this problem. I don't know really how to set it up. I attached my work. I know it is wrong but I do not know where. the correct answer is 42.2. Here is the question: A bridge over a river is supported by a hyperbolic arch which is 200 m wide at the base. The maximum...

If I am given (y-2)2= 4 (x-3), how would I find the vertex, equation of the axis of symmetry, and the direction of the opening? I'm guessing that I have to use PF=PD, but it's confusing because it looks different from other things that I have done involving PF=PD. Thanks.

I'm doing a question in my book on conics where there is a circle cutting through a parabola. There are three points S - the focus P - a point on the parabola and Q - the point where the tangent at P meets the directrix. The focus is at S[1,0] and the dirextrix is x=-1 point P is [t^2, 2t]...

Hello, Do you know a website with the most generic mathematical definitions of the conics (parabola, ellipse, hyperbola)? Thanks

I have question for you,How calculate closest distance between two ellipse in space. orbit first : r = (p1)/(1+epsilon1*cos(theta1)) second orbit : r = (p2)/(1+epsilon2*cos(theta2)) the relation between two ellipse is some euler angles call them first angle :a1 second...