Question

The ratio in which the area bounded by the curves $y^2=4x$ and $x^2=4y$ is divided by the line $x=1$ is

• A. 64 : 49
• B. 15 : 34
• C. 15 : 49
• D. None o fthese

Answer 1

Answer: (C)

15 : 49

Area = ${\int }_0^4\sqrt{4x}-\frac{x^2}{4}$
= $2\times \frac{2}{3}\times 8-\frac{(4{)}^3}{12}$
= $\frac{32}{3}-\frac{4}{3}\times 4$
= $\frac{16}{3}$
$A_1={\int }_0^1\sqrt{4x}-\frac{x^2}{4}$
= $2\times \frac{2}{3}\times -\frac{1}{12}$
= $\frac{4}{3}\times \frac{1}{12}=\frac{15}{12}$
$A_2=\frac{16}{3}-\frac{15}{12}$
= $\frac{64-15}{12}$
= $\frac{49}{12}$
$\frac{A_1}{A_2}=\frac{15}{49}$