Question

The area (in sq. units) bounded by the parabola $y=x^2-1$, the tangent at the point $(2,3)$ to it and the y-axis is

• A. $\frac{14}{3}$
• B. $\frac{56}{3}$
• C. $\frac{8}{3}$
• D. $\frac{32}{3}$

Answer 1

Answer: (C)

$\frac{8}{3}$

Here, $y=x^2-1$

So, Equation of tangent at $(2,3)$ on

$\Rightarrow$ $y=x^2-1$, is $y=(4x-5)......\left(i\right)$

$\therefore$ Required shaded area
$=area\left(△ABC\right)-{\int }_{-1}^3\sqrt{y+1}dy$

$=\frac{1}{2}\cdot \left(8\right)\cdot \left(2\right)-\frac{2}{3}{\left(\right(y+1{)}^{3/2})}_{-1}^3$

$=8-\frac{16}{3}=\frac{8}{3}$ (square units).