Parabola Midpoint: Find Equation of Locus

[Michael_Light]

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

 

[matematikeren]

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

 

[Michael_Light]

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?? ><''

 

[LCKurtz]

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.