Parabola Definition and 358 Threads

Homework Statement Here's the problem: refer to question no. 6 http://img1.uploadscreenshot.com/images/orig/5/12314183569-orig.jpg" Homework Equations I am not sure :S The Attempt at a Solution This, honestly, is a question which I have no clue how to go about... Thanks...

Note: I don't need any answer, all I want to know is whether this question is possible. Homework Statement "What is the function of the parabola which has the points (1, 1) (2, 2) and (3, 3)?" I just asked my teacher to get the question, It's not stated in my textbook. Homework...

Hi all Use the definition of a parabola and the distance formula to find the equation of a parabola with a ) directix x = -4 and focus (2,2 ) B ) directix x = 2 and focus (6,-4 ) my answer :

Hi all Use the definition of a parabola and the distance formula to find the equation of a parabola with a ) directix x = -4 and focus (2,2 ) B ) directix x = 2 and focus (6,-4 ) How i solve like this queation please hle me the steps to solve that thanks

Find the equaion of the parabola having its vertex at the origin , its axis as indicated : A ) x-axis : (-4, - 20 ) b) y - axis : (30,-15 ) C) y - axis : (-root2,3) my answer A ) we have (-4, - 20 ) that mean the focus ( - 20 , 0 ) now we do comper 4ay...

Homework Statement Sketch the graph of |x^2 - 2x - 3| Homework Equations None The Attempt at a Solution |x^2 - 2x - 3| = { x^2 - 2x + 3 x^2 - 2x - 3 >= 0 x >= 3 OR x >= -1 {-x^2 + 2x + 3 x^2 - 2x - 3 < 0 x < 3 OR x < -1 if x < -1 then y = -x^2 + 2x + 3 if -1...

Parabola for 18" aluminum mirror Help; need to configure inputs into parabola formula to machine an 18" dia., 1.5"h aluminum disc. for use as primary objective mirror in telescope.

Homework Statement Find the equation of the parabola with focus (0, -4) and directrix y = -2 i barely understand this thing. i mean how do i find the vertex. the book says D1 = focus to any point on the graph, and D2= the point on the graph to the directrix. and D1 = D2. how do i graph if...

Homework Statement What is the equation of this parabola: (10,0) ((13,27) (16,0) Homework Equations IDK what this is please help The Attempt at a Solution 0=a(10)^2+b(10)+c 0=100a+10b+c -100a-10b=c I'm stuck please help

Homework Statement A chain in the shape of y = x^{2} between x = -1 and x = 1, has density of |x|. Find M, and CM. Homework Equations The Attempt at a Solution \int^{1}_{-1}|x|dx = \int^{0}_{-1}-xdx + \int^{1}_{0}xdx = 1 I got this far and realized that I did nothing with...

stupid question, but if i know a zero of a parabola and a point it goes through, how do i find it's equation?

Hi everyone, I'm generating some hypar surfaces for a structure through parametric design techniques. In order to assess their structural abilities, I am finding their cross section curves and would like to check whether they are parabolas or not. So, in 3d space, (x,y,z) I have a curve - I...

Homework Statement write the standard form of the equation x^2-4x+8y+12=0 find the focus Homework Equations The Attempt at a Solution i have it down to (x-2)^2=-8(y-8) i'm not sure if you have to multiply the -8 on the right side of the equations by 4 since the focus is 1/4a

Hello, I'm new here and wasn't sure if this should be put into the homework section. It's not a homework question but the nature of the problem is homework-ish in nature I suppose. Anyway I'm trying to understand why a velocity vector along a parabola would have the same initial velocity as...

Homework Statement My question is on the last bit of Apostol's proof, in his book Calculus Vol I 2nd ed, where he shows that the area under the parabola = b^{3}/3 where b is the base of the rectangle enclosing the parabola. The bit I am confused about is where his contradiction...

hello everyone, :confused:i'm having can't seem to solve these two questions... 1) Find the equation of the tangent of the parabola y^2= 4px, perpendicular to the lines 4Y- X + 3=0, and find the point of contact? 2) Find the equation of the tangent to the parabola Y^2= 10x, at the...

Hi everybody we know that if we have an object sliding on a frictionless ramp, the acceleration force will be constant, and it equals to a=g * sin(theta) where theta is the ramp angle w.r.t. the ground so the path of motion in this problem can be written mathematically as a...

Homework Statement i am given the equation of a parabola to be y=2x^2-2x+3 and asked to sketch the parabola Homework Equations y=1/2(l-p)(x-k)^2+(l+p)/2 (l+p)/2=h vertex is at (k,h) equation of the directrix is y=p distance[(k,h) to y=p]=distance[(x,y) to (k,h)] The Attempt...

Homework Statement This problem is from the Australian HSC mathematics extension 2 exam. Q6ciii) It states: Find the focus, S, of the parabola y^2=r^2+c^2-2cx where r and c are constants. The Attempt at a Solution I couldn't figure out how to convert this into the parabola focus...

Homework Statement Where does the normal line to the parabola y= x - x^2 at the point (1,0) intersect the parabola a second time? Illustrate with a sketch Homework Equations y= x - x^2 The Attempt at a Solution y' = 1-2x slope of tangent = -1 (after substituting value of x in...

Homework Statement Prove that a vertical line and a line going from a point on a parabola to the focus of the parabola form equal angles with the tangent line of the point on the parabola. Homework Equations Focus = 1/4a (maybe relevant) The Attempt at a Solution I know how to...

For a parabola whose Directrix is given by the equation x=p and whose Focus is (h,k). Is this by any chance the correct general form of the parabola? x=1/2(h-p) [y^2 - 2yk + h^2+k^2-p^2]

The parabola y = x2 is rotated anti-clockwise about the origin through the angle 30o. What is the new equation of the new curve (relative to the standard basis)?

Homework Statement Use completing the square method to rewrite the equation of the parabola y^2 – 4y – 44 = 16x in the form (y-y0)^2 = 4A(x-x0) Hence find: a) the coordinates of the vertex b) the coordinates of the focus c) the equation of the line that passes through the focus...

Homework Statement a cannon launches a projectile. H, is the height in metres that the cannon ball is above the horizon by t seconds. h= -0.75t^2 + 16t + 3 Homework Equations What is the maximum height reached by the cannonball? The Attempt at a Solution Ok so i tried completing...

Homework Statement For a any parabola with the equation y=kx^{2} I'm trying to find a curve that intersect every point of the parabola at right angles. Homework Equations For a perpendicular intersection the slope is -\frac{1}{m}The Attempt at a Solution I took the derivative and then took...

When you take a paper strip, put it on the flat surface (table), and contract it so it stands up - is it parabola or something else?

Homework Statement I am a bit rusty on parabolae. I am doing a question on projectiles and have found the coordinates of the vertex of a parabola as: (\frac{(v_0)^2\sin\alpha\cos\alpha}{g},\frac{(v_0)^2(\sin^2\alpha)}{2g}) The question now requires you to show that the distance...

1. The graph of a quadratic function (a parabola) has x-intercepts -1 and 3 and a range consisting of all number less than or equal to 4. Determine an expression for the function. 2. none 3. I do not know how to use the intercepts and the range and manipulate it into a function...

You have a flat wooden surface, some rope, some nails and a pencil - how do you draw parabola using just that?

I read a Wikipedia article titled "Parabola" that listed an equation of the form: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 How is this derived? or where did it come from?

Homework Statement A circle with radius 1 inscribed in the parabola y=x^2. Find the center of the circle.Homework Equations equation of the parabola: y=x^2 circle: (x-h)^2 + (y-k)^2 = 1 The Attempt at a Solution After ghosting the forums and reading through every post with this exact same...

Homework Statement The vertex of the parabola y^2=2px is the center of an ellipse. The focus of the parabola is an end of one of the principle axes of the ellipse, and the parabola and ellipse intersect at right angles. Find the equation of the ellipse. Homework Equations...

Homework Statement http://img40.imageshack.us/img40/39/20688555.gif a) Show that if C is any straight line through (0,0) then \lim_{(x,y) \to (0,0)} along C exists and equals 1. b) Show that the limit as (x,y) -> 0 doesn't exist. Homework Equations The Attempt at a...

See, there is an equation which is f(x) = x^2 - 5x + 6. On the points 2 and 3 of the x axis, they reach 0. So where is the vertex? I'm guessing its -.25, but just to make sure i had to ask. Well, our class seemed to have a lot of it and our teacher, Ms. Knudsvig, didn't know.

Find the equation of a parabola with the following characteristics: range Y <= 8 x-coordinate of the turning point is -4 y-intercept = -6 I have tried to substitute all the information into y = a(x-p)^2 + q which gives me y = a(x+4)^2 + q and substituted the y-intercept into the...

Homework Statement Show that the transformation _ __ _ __ | 0 -2 1 || x | | -2 2 0 || y | |_2 -2 1 _||_ 1_| takes all points on parabola y2=x onto the unit circle x2+y2=1 Homework Equations The Attempt at a Solution I can't find out what to do I just...

Homework Statement In each part, evaluate the integral \int(3x+2y)dx+(2x-y)dy (A) The line segment from (0,0) to (1,1). (b) The parabolic arc y=x^2 (c) The curve y=sin(pi(x)/2) from (0,0) to (1,1) (D) The curve x=y^3 from (0,0) to (1,1). Homework Equations \int...

2. Find the shortest distance from the point (1,4) to a point on the parabola y^2 = 2x Not really sure what to do here next. I'd imagine i might have to fuse implicit differentiation? But not really sure.

Homework Statement 1. It is a word problem I need done by tomorrow morning. so please help: A new bridge is being constructed. The space between the support needs to be 1050 feet; the height at the center of the arch needs to be 350 feet. An empty tanker needs a 280 foot clearance to pass...

1" ball hitting Parabola If a 1" ball hits the inside of a parabola, what part of the ball hits the focal point? Is it the edge that strikes the inside of the parabola or the center of the ball? Thank You

Homework Statement Write the equation in standard form for the parabola with an axis of symmetry y=0 and focus(-5,0). Homework Equations I think ax^2+bx+c. Also maybe x = -b/2a. But I don't know how to apply these. The Attempt at a Solution I know that focus and vertex lie on...

To the moderator: This isn't a HW question, but it probably sounds like one, so I appologize. Please move this to the HW forum if need be. I have an integration domain inside three intersecting curves. Two of the curves are straightlines and the third is a parabola. These three boundaries...

A Tangent to the parabola y = 3x^2 - 7x + 5 is perpendicular to x + 5y - 10 = 0 Determine the equation of the tangent i really don't know where to start!

Homework Statement I'm still kind of confused with projectile motion. I know when you throw something, you throw it at an angle and will have a negative parabola effect. An exception to when you throw something up at a 90° angle where it will go up vertically and come down vertically, with no...

Homework Statement Write a function for d(x), the vertical distance between the two curves, and find the minimum value of d(x). Homework Equations The equation for parabola one is y = x^2 + 6, for parabola two, y = -(x-2)^2 + 6 The Attempt at a Solution The answer in the back...

1. I need to find the equation of a parabola with a vertex of (-3,-2). It has to open down. 2. I understand of hopefully will understand it. 3. My answer was y=-3x Squared -3x-2 Which I found to be wrong.

Homework Statement In an over hand serve, the ball starts from a point 2m above the ground and travels a horizontal distance of 20m before it strikes the floor. The ball travels in a parbolic path and reaches its highest point after traveling a horizontal distance of 9m as show in the...

Homework Statement find the focus and directrix of the parabola: (y+2)^2 = 16(x-1) Homework Equations (y-k)^2= 4a(x-h) focus: ( h+a,k) vertex: (h,k) The Attempt at a Solution k=-2,h=1,a=16/4=4!, vertex at (1,-2) focus ( 5,-2) does that mean that i solved the problem or do...

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...