Parabola Midpoint: Find Equation of Locus

  • Thread starter Thread starter Michael_Light
  • Start date Start date
  • Tags Tags
    Parabola
Click For Summary

Homework Help Overview

The problem involves finding the equation of the locus of the midpoint of a segment PQ, where P is a point on a variable tangent to the parabola defined by the equation y² = 4ax, and Q is the intersection of this tangent with the y-axis. There is a discrepancy between the original poster's answer and a provided answer.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to derive the locus equation but questions the correctness of their result compared to another provided answer. Some participants suggest looking at external resources for similar problems, while others express a desire for direct assistance with the original question.

Discussion Status

The discussion is ongoing, with participants sharing their findings and seeking clarification. There is no explicit consensus on the correct answer, but some participants have independently arrived at the same conclusion as the original poster.

Contextual Notes

Participants are working under the constraints of homework guidelines, which may limit the type of assistance they can provide. There is a focus on understanding the derivation of the locus rather than simply confirming answers.

Michael_Light
Messages
112
Reaction score
0

Homework Statement



A variable tangent at P to the parabola y2=4ax meets the y-axis at Q. Find the equation of the locus of the midpoint of PQ. As shown below, my final answer is 2y2=9ax but the answer provided is y2=9ax. Can anyone correct me?

Homework Equations


The Attempt at a Solution



DSC00596 - Copy.jpg
 
Physics news on Phys.org
Michael_Light said:

Homework Statement



A variable tangent at P to the parabola y2=4ax meets the y-axis at Q. Find the equation of the locus of the midpoint of PQ.


As shown below, my final answer is 2y2=9ax but the answer provided is y2=9ax. Can anyone correct me?

Homework Equations





The Attempt at a Solution



View attachment 34238

Might I surgest you take look at this website here.

http://home.scarlet.be/~ping1339/parabola.htm

It deals with a very simular problem :)

/Fred
 
matematikeren said:
Might I surgest you take look at this website here.

http://home.scarlet.be/~ping1339/parabola.htm

It deals with a very simular problem :)

/Fred

Its a very good website... but would you kindly help me with my question first?? ><''
 
Michael_Light said:

Homework Statement



A variable tangent at P to the parabola y2=4ax meets the y-axis at Q. Find the equation of the locus of the midpoint of PQ.


As shown below, my final answer is 2y2=9ax but the answer provided is y2=9ax. Can anyone correct me?

Homework Equations





The Attempt at a Solution



View attachment 34238

If it's any help to you, I worked it myself without looking at what you did and I got the same answer you did.
 

Similar threads

Tangent line and normal on a parabola
  • · Replies 10 ·
Replies
10
Views
3K
Proving Locus of Middle Points of Chords on Parabola
  • · Replies 2 ·
Replies
2
Views
2K
Identifying the equation of a parabola
  • · Replies 2 ·
Replies
2
Views
2K
What is the minimum distance between a tangent and normal of a parabola?
  • · Replies 15 ·
Replies
15
Views
5K
Locus of mid point of parabola and straight line
  • · Replies 9 ·
Replies
9
Views
5K
Midpoint Property of Tangents to Parabolas
  • · Replies 14 ·
Replies
14
Views
2K
Triangle formed by tangents to a parabola
  • · Replies 3 ·
Replies
3
Views
3K
Parabola Find a the value of a
  • · Replies 2 ·
Replies
2
Views
2K
Finding the focus of a parabola given an equation
  • · Replies 4 ·
Replies
4
Views
2K
Find Minimum Value of T^2 in Normal to Parabola y^2 = 4ax at (at^2, 2at)
  • · Replies 3 ·
Replies
3
Views
3K