Question

The coordinates of the points on the curve \(4y = x^2\) that are nearest to the point \((0,5)\) are ...

• A. \((-2\sqrt{3},3)\)
• B. \((2\sqrt{3},-3)\)
• C. \((3,2\sqrt{3})\)
• D. \((2\sqrt{3},2)\)

Hint:

Relate dS/dt to dr/dt using S = 4 pi r squared.

Answer 1

The Correct Option is A

Step 1: Use the radius form of area:
Since $S = 4\pi r^2$, the rate of change of the radius is $\frac{dr}{dt} = \frac{dS/dt}{8\pi r}$.

Step 2: Numbers:
With $r = 2$: $\frac{4\pi}{16\pi} = \frac14$ cm/s (B).

Final Answer:
0.25 cm/s. \[ \boxed{0.25\text{ cm/s}} \]