Question

Which of the following points lies on the parabola $y^2=4x$?

• A. $(1,1)$
• B. $(1,-1)$
• C. $(1,3)$
• D. $(\frac{1}{4},1)$

Answer 1

Answer: (D)

$(\frac{1}{4},1)$

For a point $(h,k)$ to lie on the parabola $y^2=4x$, $k^2-4h=0$

For the point $(1,1)$, $k^2-4h=1-4=-3\ne 0$.

So, the point $(1,1)$ does not lie on the the parabola.

Similarly, for the points $(1,-1)$ and $(1,3)$, $k^2-4h\ne 0$.

For the point $(\frac{1}{4},1)$, $k^2-4h=1-4\left(\frac{1}{4}\right)=0$.

So, the point $(\frac{1}{4},1)$ lies on the the parabola.

So, the answer is option (D).