Parabola Definition and 358 Threads

HI! I'm not sure if this can go in precalculus or not because I'm from Australia, and our Maths subjects don't get that specific until university level. 1. Homework Statement For my assignment on quadratic functions, I have to find the equation (the the form of ax^2+bx+c) for a table of...

How can I solve the equation of a parabola when the focus and Latusrectum are given?

Let $$y = 2x^2 + 4x + \tfrac{7}{4}$$ and line $$p$$ a normal which go through the point $$(X, Y)$$. Find the regions in $$xy$$-plane where there are either 3 distinct normals or only 1 normal.

Find all the normals of function $$y = 2x^2 + 4x + \tfrac{7}{4}$$ which goes through the point $$\left( 3, \tfrac{15}{2} \right)$$.

I do not understand this: An ellipse has a directrix? A parabola, for sure. This is part of the definition and we can derive the equation of a parabola using the meaning of Directrix and the meaning of Parabola. How does a directrix work for an ellipse?

Homework Statement If the normal at P(ap^2 ,2ap) to the parabola y^2 = 4ax meets the curve again at Q(aq^2, 2aq), show that p^2 +pq+2=0 Homework Equations Point-slope form The Attempt at a Solution I tried putting y=2aq and x=aq^2 but I can seem to simplify the whole thing other than...

Homework Statement Alright, so the equation of a parabola is y = 1/4p*x^2, P being either an x or y value, and the other x or y being zero. Let's say that x^2 = 16y. If you divide both sides by 16, you get y = x^2/16, which can be simplified to y = 1/16*x^2. This is in the format of a parabola...

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) =...

The graph of $y=(x-2)^2 - 1$ is given, then they say use this graph for problem 7 Next is 7) $f(x) =\frac{1} {g(x)} $ ? Step one restrictions $y> \ge - 1$ Step two Equation Solution? Step three: Domain:= $\left(-\infty, +\infty\right)$ Vertical Asymptopes at: none What's with the?

Homework Statement Hello! Please, help me to get through equations. I can't derive the equation in the way suggested. Here is the definition: So, if vertex is at (h, k) and there is a given point on a parabola at (x; y), then focus is at (h; k + p), and point of a directrix is at (x; k -...

Hey, all. I'm wanting to type up a few ways to solve a neat Kleppner & Kolenkow problem, and I'd like to put a diagram I've drawn in. Here is what I'd like to insert...

Homework Statement The triangle formed by the tangents to the parabola y2=4ax, at the ends of the latus rectum and the double ordinate through it's focus is: 1) equilateral 2) acute angles isosceles 3)right angled isosceles 4) dependent on value of a Homework Equations...

This sounds like a dumb question. I have come to accept projectiles form parabolas but I need someone to explain why they form this shape

Homework Statement I'm trying to find the vertex of this parabola: y^2-12=12x The Attempt at a Solution Initially I tried to take the derivative and find the vertex by finding where it the function is zero, but apparently that does not work in this situation. Is it because it is not in...

Whats's the volume under the revolving parabola y=ax2. R is xmax. $$V=\int_0^R\pi xdx\cdot y=\pi\int_o^R x\cdot Ax^2dx=\pi A\frac{R^4}{4}$$ Volume should be relative to R3. and if i had, for example, y=Ax3 then, according to my calculation i would get relative to R7 and so on.

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1. The trajectory of a rock thrown from a height with an initial speed of 20.9 m/s is shown in the figure below. Evaluate the magnitude of the gravitational field at the surface of the planet. The planet has no atmosphere...

I know a tangent drawn on parabola having equation like y^2=4ax is y=mx+(a/m) which provides c=a/m Then how is it going to turn for equation like x^2=4ay? From my derivation it will be like -c=am^2 when the equation of tangent is y=mx+c. The derivation comes from the following: y=mx+c or...

Homework Statement The sketch on the previous page shows the graph of a function f, which is a parabola with vertex R, and the graph of a function g, which is a straight line defined by g(x)=-(1/2)x. The graphs of f and g intersect at P and O(the origin). The function f is defined by...

Homework Statement The orthocentre of the triangle formed by points t1,t2, t3 on the parabola y2 = 4ax is vertex Origin Focus (1,0) Homework Equations NA The Attempt at a Solution The points can be taken anywhere, So orthocentre can be formed anywhere isn't it?

Homework Statement Hey all, I've been learning some incredibly INCREDIBLY basic calculus on my own, so please take it easy on my stupidity. So here's what I was wondering. In a 1 dimensional theoretical system, let the acceleration experienced by an object = A, with the signage +/- indicating...

Homework Statement [/B] Find equations of both lines through the point (2,-3) that are tangent to the parabola y=x2+x. Homework Equations Slope formula: (Y2-Y1)/(X2-X1) = M The Attempt at a Solution Here's what I think I need to do. First I think I need to find the derivative of the...

Homework Statement The Attempt at a Solution I would guess it is -b/2a but I have gotten this incorrect. Maybe I have to figure out what the parabola equation is and apply it into the axis of symmetry. Assuming that is correct how would I find that? Thanks[/B]

Homework Statement A skier travels with a constant speed of 6 m/s along a parabolic path y= x2/20. Find the acceleration of the skier when he is at (10,5). Neglect the size of skier. Homework Equations dy/dx is slope of parabola. In a straight line if body has distance covered=x, then velocity...

Homework Statement So I am doing a trajectory lab. I take a ball and release it from the ramp that is on the table and then measure the distance. The thing is when I graph the angle of the ramp vs the distance the ball has fallen I get parabola. And the correlation of parabola is 0 Homework...

I want to calculate moment of inertia of an angle L bent in form of a parabola. The parabola is attatcehd to a H section bent in form of a circle such that the center of circle and focus of parabola lie at the same point. I want to know how to calculate the moment of inertia for the whole assembly

I read that concave mirrors are part of a sphere, and concave mirrors can also be expressed in a parabola equation, but a parabola equation is expressed as #4py=x^2# and a circle as #x^2+y^2=R^2#. So the two can't be the same right? Can someone please explain this? Thank you in advance :)

So I was doodling around and came up with a problem of finding an equation for a tilted parabola. Basically, a parabola in xy plane which was rotated around a line that goes through points (1,0) and (0,1), making the curve a 3D one. I realize that this curve is a subset of points that define a...

hi! i don't quite know how to start solving for this. i understand the problem and what it's asking for but i have no idea how to start solving for it. In a volleyball game, a player from one team spikes the ball over the net when the ball is 10 feet above the court. The spike drives the ball...

Homework Statement A line passing through the point (1,0) cuts the curve Y^2=4x at two points A and B. Find the equation of the locus of the mid-point of AB. Homework EquationsThe Attempt at a Solution the graph is parabola, the solution should also be a parabola with x-intercept at (1,0)...

If incoming light to a parabola is parallel to the central axis the light is reflected through the focal point and the back to its source. What about light coming in not parallel to the central axis. What path do these rays take?

Hello friends. This is my first post. I am given the following problem: Find the equation of parabola with vertex (2, 1) and focus (1, -1) I have tried to solve this question in this way: Since vertex is mid point of Focus and the point which touches the Directrix. From this, I calculate that...

Homework Statement If the normal to the parabola y^2 = 4ax at the point (at^2 , 2at) cuts the parabola again at (aT^2, 2aT), then minimum value of T^2 is ans: 8 I got the answer but I don't know why it should be the answero_O? Homework Equations Equation of normal to the parabola in parametric...

i don't know whether this goes here or under the calculator forum. i want to graph x=t y=1/(1+t^2) and z=t^2 and i keep getting a parabola. is that right because the drawing in my book is like a slanted parabola.

The general equation of a parabola is: (y - y1) = A(x - x1)^2 A is the scaling factor y1 is the y coordinate of a vertex/point on the parabola x1 is the x coordinate of a vertex/point on the parabola My two questions are: 1. Can (x,y) be any point on the graph ? 2. If so, then if x -...

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Homework Statement Hi! I am doing some problems to practice for a math competition, and I'm wondering if I did this correctly. I don't really have an answer sheet, so I have no way of knowing whether I'm right. If you would please review it, that would be cool! It reads: There are...

The general equation of the parabola has the form $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ with $B^2 = 4AC$ what is the coordinate of the vertex of the parabola or in other word how to determine the vertex of a given parabola for example $4x^2 + 4xy + y^2 - 5x + 7y + 11 =0 $ Thanks.

Homework Statement A particle is moving along a parabola y = x2 so that at any time vx = 3 ms-1. Calculate the magnitude and direction of velocity and acceleration of the particle at the point x = 2/3 m. Homework Equations Kinematics The Attempt at a Solution vx = 3 (given) y = x2 so vy =...

The base of a solid is the region bounded by the parabola $$y^2=4x$$, and the line $$x=2$$ . Each plane section perpendicular to the x-axis is square. (I assume this means the cross-section of the solid will be square) then we are not revolving but slicing. The volume of the solid is? (the...

I am not able to solve the following problem #1) Prove that the normal to parabola y2=4ax at (am2,-2am) intersects the parabola again at an angle tan-1(m/2) What I am thinking is to solve the equation of parabola and equation of normal y=mx-am-3-2am simultaneously and at that point I will...

Homework Statement Sketch the curve C defined parametrically by ##x=t^{2} -2, y=t## Write down the Cartesian equation of the circle with center as the origin and radius ##r##. Show that this circle meets the curve C at points whose parameter ##t## satisfies the equation ##t^{4} -3t^{2}...

Homework Statement The title.Homework Equations ##y=mx+c## $$\frac{dy}{dx}(kx^2)=2kx$$ The Attempt at a Solution https://www.physicsforums.com/attachment.php?attachmentid=69745&stc=1&d=1399976415 I have proved that the angle of reflection will be a° since the angle of incidence=a° The picture...

Homework Statement Find the parametric equations for the portion of the parabola y=x^2 from (-1,1) to (3,9) Homework Equations None that I know of. The Attempt at a Solution Using knowledge of parametric equations I am not sure how to start. My teacher never went over this...

the normal at a point N of the parabole: y2 = 2px to the curve at another point M. calculate the intercept of N when the length of MN is minimal. Answer sqrt (2) p

Hello, I am supposed to find the equation of a parabola with the points (8,10)(11,10)(10,20/3). I have tried putting these values into y=ax^2+bx+c, but get different answers each time, like c=-160, which is not right! A step by step explanation would be greatly appreciated, as I am very unsure...

Homework Statement The point of suspension of a simple pendulum of length l and mass m is constrained to move on a parabola z = ax^2 in the vertical plane. Derive a Hamiltonian governing the motion of the pendulum and its point of suspension. This is a two-dimensional problem...

Find the curve coordinates of the point nearest to P in the curve 2y2 = 5(x+1) P(0,0) Book answer (-1,0) ok (x-0)2+ (y-0)2 = D D = (x)2+ (y)2 and (y)2 = -x2 Now -x2 = 5/2(x+1) But derivating I don't get the answer or ansa

Find the curve coordinates nearest to P a)x2 = y P(3,0) ok to the boox exercise model I must do so (x-3)2+ (y)2 = D then x2-6x +9+y2 = D introducing y into x y-6sqrt(y) +9 + (y)2 = D derivating 1-3/(sqrt(y) +0+2y mcm = sqrt(y) -3 +2y = 0 solving sqrt(y) = -2y+3 Squaring y =...

Homework Statement Find the largest circle centered on the positive y-axis which touches the origin and which is above y=x^2 Homework Equations equation of a circle: r^2=(x-a)^2+(y-b)^2 equation of a circle centered on the y-axis: x^2+(y-b)^2=r^2 equation of a parabola: y=x^2 The...