The area bounded in the first quadrant by the normal at` (1,2)`on the curve `,y^2=4x,x-`axis &the curve is given by (A) `10/3` (B) `7/3` (C) `4/3` (D) `9/2`

Options

A. 10/3
B. `7//3`
C. `4//3`
D. None of these

Answer

A

Explanation

Equation of normal at (1, 2 ) is ` x + y = 3, ` which meets X -axis at ` N ( 3, 0 ) `
` therefore QN = 2, PQ = 2 `

` therefore ` Required area
= Area of ` Delta PQO ` + Area of ` Delta PQN `
` = int _ 0 ^ 1 sqrt (( 4x )) dx + ( 1 )/( 2 ) * 2 * 2 = ( 10) /( 3) `