The tangent and normal to the ellipse 3 x 2 + 5 y 2 = 32 at the point P 2 , 2 meet the x -axis at Q and R , respectively. Then the area (in sq. units) of the triangle P Q R is:

Step-by-step solution

The equation of tangent and normal to the ellipse x 2 a 2 + y 2 b 2 = 1 at a point x 1 ,   y 1 are respectively x x 1 a 2 + y y 1 b 2 = 1 and a 2 x x 1 - b 2 y y 1 = a 2 - b 2 . The given ellipse is 3 x 2 + 5 y 2 = 32 ,     ⇒ 3 x 2 32 + 5 y 2 32 = 1 . Hence, the tangent and normal to the ellipse 3 x 2 32 + 5 y 2 32 = 1 at 2 ,   2 are respectively 3 × 2 × x 32 + 5 × 2 × y 32 = 1 and 32 × x 3 × 2 - 32 × y 5 × 2 = 32 3 - 32 5 Hence, the tangent is 3 x +