Question

At ........... point on the parabola $x^2 = 4y$. the rate of increase of the x-coordinate is the same as the rate of the increasing y-coordinate.

• A. $(2, 1)$
• B. $(- 3, 1)$
• C. $(- 2, 1/4)$
• D. $(7/4, 1/4)$

Answer 1

Answer: (A)

$(2, 1)$

Answer 2

As given $\frac{dx}{dt}=\frac{dy}{dt}$ Now $x^{2}=4y$ $\Rightarrow 2x \frac{dx}{dt}=4 \frac{dy}{dt}$ $\Rightarrow 2x=4$ $\Rightarrow x=2$ $\therefore 4y=\left(2\right)^{2}=4$ $\Rightarrow y=1$ $\therefore$ reqd. point is $\left(2, 1\right)$