# Thread: Parametric Parabola: Show that SP = TS

1. ## Parametric Parabola: Show that SP = TS. ! simple

Hi, I'm a newbie.

Okay, I'm sorta struggling with this question:

P is a point on the parabola x^2 = 4ay
The tangent at P meets the axis at T. If the focus is at S, show that SP = TS.

I have gathered the following coordinates:

P = (2ap, ap^2)
T = (ap, 0)
S = (0,a)

Unfortunately, when I used the distance formula, it shows that the 2 lines are not equal.

Does anyone have a clue how to do this?

Thanks

yeah.. I know this is a simple question (yet I can't solve it!).. please.. nice comments only. I've been attacked on other forum websites before, because of my stupidity

2. Originally Posted by differentiate
The tangent at P meets the axis at T.
Hi

Don't you think that it is the y-axis instead of the x-axis ?

3. hmmm... if it were the y axis, that would mean that T = (0,-ap^2)

SP = sqrt (2ap-0)^2 + (ap^2 - a)^2
= 4a^2(p^2) + a^2(p^4) + a^2 - 2a^2(p^2)
= 2a^2(p^2) + a^2(p^4) + a^2

TS = sqrt (-ap^2-a)^2
a^2(p^4)+a^2 + 2a^2(p^2)

SP = TS

ahhh I see. Thanks

4. ## ok...

I thank both replies and the interesting debate.