Parabola Midpoint: Find Equation of Locus

  • Thread starter Thread starter Michael_Light
  • Start date Start date
  • Tags Tags
    Parabola
AI Thread Summary
The discussion revolves around finding the equation of the locus of the midpoint of segment PQ, where P is a point on the parabola y²=4ax and Q is where the tangent at P meets the y-axis. The original poster believes their answer is 2y²=9ax, while the provided answer is y²=9ax. Participants suggest reviewing a helpful website for similar problems but also express a desire to focus on resolving the original question. One user confirms they arrived at the same answer as the original poster, indicating a potential issue with the provided solution. The conversation highlights the need for clarification on the correct equation of the locus.
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.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

Tangent line and normal on a parabola
Replies
10
Views
3K
Proving Locus of Middle Points of Chords on Parabola
Replies
2
Views
2K
Identifying the equation of a parabola
Replies
2
Views
2K
What is the minimum distance between a tangent and normal of a parabola?
Replies
15
Views
4K
Locus of mid point of parabola and straight line
Replies
9
Views
4K
Midpoint Property of Tangents to Parabolas
Replies
14
Views
2K
Triangle formed by tangents to a parabola
Replies
3
Views
3K
Parabola Find a the value of a
Replies
2
Views
1K
Finding the focus of a parabola given an equation
Replies
4
Views
2K
Find Minimum Value of T^2 in Normal to Parabola y^2 = 4ax at (at^2, 2at)
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top