Question

The areaenclosed by the parabola $y ^ { 2 } = 8 x$ and the line $y = 2 x$ is

• A. $\frac { 4 } { 3 }$
• B. $\frac { 3 } { 4 }$
• C. $\frac { 1 } { 4 }$
• D. $\frac { 1 } { 2 }$

Answer 1

Answer: (A)

$\frac { 4 } { 3 }$

Answer 2

Solve the equation $y ^ { 2 } = 8 x$ and the line $y = 2 x$ we get the point of intersection. Then find the required area bounded by this region. It is$\frac { 4 } { 3 }$.

Trick : Required area$= \frac { 8 ( 2 ) ^ { 2 } } { 3 ( 2 ) ^ { 3 } } = \frac { 32 } { 24 } = \frac { 4 } { 3 }$ [$\bullet \bullet$ Area bounded by $y ^ { 2 } = 4 a x$ and $y = m x$ is $\frac { 8 a ^ { 2 } } { 3 m ^ { 3 } }$Here $a = 2 , m = 2$ ]