Question

The area bounded by the normal at $(1,2)$ to the parabola $y^2=4x$, x-axis and the curve is given by

• A. $\frac{10}{3}$ sq. units
• B. $\frac{7}{3}$ sq. units
• C. $\frac{4}{3}$ sq. units
• D. $\frac{1}{3}$ sq. units

Answer 1

The correct option is A

$\frac{10}{3}$ sq. units

Equation of normal to the given parabola at $(1,2)$ is $x+y=3$

It meets x-axis at $N(3,0)$

$\therefore QN=2,PQ=2$

$\therefore$ Required Area = area of $\Delta PQO$ + Area of $\Delta PQN$

$={\int }_0^1\sqrt{4x}dx+\frac{1}{2}\times 2\times 2=\frac{10}{3}$