Question

Let A be the area enclosed between the curves $y^2=4x$ and $x^2=4y$. Then

• A. A is divided by the line x = 1 in the ratio 15 : 28
• B. A is divided by the line x = 1 in the ratio 15 : 49
• C. $A=\frac{64}{3}$
• D. $A=\frac{16}{3}$

Answer 1

Answer: (B), (D)

The correct options are
B A is divided by the line x = 1 in the ratio 15 : 49
D $A=\frac{16}{3}$

$A=\frac{16a^2}{3}=\frac{16}{3}$
$A_1={\int }_0^1(\sqrt{4x}-\frac{x^2}{4})dx=\frac{5}{4}$
$A_2={\int }_1^4(\sqrt{4x}-\frac{x^2}{4})dx=\frac{49}{12}$
$\Rightarrow A_1:A_2=15:49$