Question

If the tangents on the ellipse 4x² + y² = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a² is equal to:
(A) 2/17
(B) 4/17
(C) 64/17
(D) 128/17

Answer 1

Answer:

A

It a the answer to this question is a

Answer 2

If the tangents on the ellipse 4x² + y² = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a² is equal to:

Given,

The equation of ellipse 4x² + y² = 8

differentiating the above equation, we get,

$4 \times 2x + 2y \dfrac{dy}{dx} = 0\\\\4x + y \dfrac{dy}{dx} = 0\\\\\8x + 2y \dfrac{dy}{dx} = 0 \\\\ \dfrac{dy}{dx} = -\dfrac{4x}{y}$

tangents at the points (1, 2) and (a, b) are perpendicular to each other

we have, $(-\dfrac{4}{2}) \times (-\dfrac{4a}{b}) = -1$

b = -8a

as (a, b) lies on the ellipse, we have,

4a² + b² = 8

4a² + (-8a)² = 8

4a² + 64a² = 8

68a² = 8

∴ a² = 2/17

Therefore option (A) is correct.