The area (in sq. units) bounded by the parabola y = x2 - 1, the tangent at the point (2, 3) to it and the y-axis is :

Question

The area (in sq. units) bounded by the parabola y = x2 - 1, the tangent at the point (2, 3) to it and the y-axis is : (A) (14/3) (B) (56/3) (C) (8/3) (D) (32/3)

Tardigrade Admin · Accepted Answer

Equation of tangent at (2,3) on y = x2 - 1, is y = (4x - 5) .....(i) ∴ Required shaded area =ar (Δ ABC) - ∫3-1 √y+1dy = (1/2) .(8).(2)- (2/3) ((y+1)3/2)3-1 = 8 - (16/3) = (8/3) (square units)

Q. 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 :

$\frac{14}{3}$

$\frac{56}{3}$

$\frac{8}{3}$

$\frac{32}{3}$

Equation of tangent at (2,3) on
$y = x^{2} - 1$ , is $y = (4 x - 5)$ .....(i)
$∴$ Required shaded area
$= a r (Δ A BC) - \int_{- 1}^{3} y + 1 d y$
$= \frac{1}{2} . (8) . (2) - \frac{2}{3} ((y + 1)^{3/2})_{- 1}^{3}$
$= 8 - \frac{16}{3} = \frac{8}{3}$ (square units)

Q. The area (in sq. units) bounded by the parabola y=x2−1, the tangent at the point (2,3) to it and the y-axis is :

314​

356​

38​

332​