If the point P on the curve, 4 x 2 + 5 y 2 = 20 is farthest from the point Q 0 , - 4 , then P Q 2 is equal to

Step-by-step solution

Give ellipse x 2 5 + y 2 4 = 1               . . . 1 Let P 5 cos θ ,   2 sin θ Ellipse (1) Given Q 0 ,   - 4 P Q 2 = 5 cos θ 2 + 2 sin θ 2 2 ⇒ P Q 2 = 5 cos 2 θ + 4 sin 2 θ + 16 cos 2 θ + 16 ⇒ P Q 2 = 4 + cos 2 θ + 16   sin θ + 16 = 1 - sin 2 θ + 16   sin θ ⇒ P Q 2 = 17 - sin 2 θ + 16   sin θ ⇒ P Q 2 = 17 - sin 2 θ - 16   sin θ ⇒ P Q 2 = 21 sin &#9