P(2ap,ap^2) is a point on the parabola x^2=4ay

The normal at P cuts the x axis at S and the y axis at T.

S= (ap(2+p^2),0)

T= (0, a(2+p^2))

Find the value(s) of p such that P is the midpoint of ST

Thanks Nath

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- July 7th 2006, 02:02 AMnath_quamParabola/Normals
P(2ap,ap^2) is a point on the parabola x^2=4ay

The normal at P cuts the x axis at S and the y axis at T.

S= (ap(2+p^2),0)

T= (0, a(2+p^2))

Find the value(s) of p such that P is the midpoint of ST

Thanks Nath - July 7th 2006, 06:43 AMmalaygoelQuote:

Originally Posted by**nath_quam**

In other words, or

Keep Smiling

Malay - July 7th 2006, 09:17 AMSoroban
Hello, Nath!

They already did the groundwork for us . . . the rest is easy.

[I got the same answers, Malay!]

Quote:

is a point on the parabola

The normal at cuts the x-axis at and the y-axis at

Find the value(s) of such that is the midpoint of

I assume you know the Midpoint Formula . . .

Given two points and , the midpoint of is: .

We have: .

The midpoint is: .

Since we want , we have: .

If two points are equal, their corresponding coordinates are equal.

Equate 's: .

. . Divide by

Equate 's: .

. . Divide by

Therefore: .

- July 7th 2006, 04:56 PMnath_quam
Thanks Guys

- July 10th 2006, 04:39 AMnath_quamJust Quickly
Is a possible answer p = 0

- July 10th 2006, 04:43 AMmalaygoelQuote:

Originally Posted by**nath_quam**

Keep Smiling

Malay