Conic Sections Question 516

Question: $ x-2=t^{2},\ y=2t $ are the parametric equations of the parabola

Options:

A) $ y^{2}=4x $

B) $ y^{2}=-4x $

C) $ x^{2}=-4y $

D) $ y^{2}=4(x-2) $

Show Answer

Answer:

Correct Answer: D

Solution:

Here $ \frac{y}{2}=t $ and $ x-2=t^{2} $

therefore $ (x-2)={{( \frac{y}{2} )}^{2}} $

therefore $ y^{2}=4(x-2) $ .