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
Hello, Nath!
They already did the groundwork for us . . . the rest is easy.
[I got the same answers, Malay!]
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: .