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 ______.

विकल्प

• `2/17`

• `4/17`

• `64/17`

• `128/17`

Answer 1

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 `underlinebb(2/17)`.

Explanation:

4x² + y² = 8

Tangent at (1, 2),

4x.1 + y.2 = 8

2x + y = 4  ...(i)

m₁ = –2

Tangent at (a, b),

4xa + by = 8  ...(ii)

m₂ = `(-4a)/b`

m₁m₂ = –1

`-2((-4a)/b)` = –1

–8a = b  ...(iii)

(a, b) lies on ellipse

4a² + b² = 8

Equation (iii) and (iv),

64a² = b²

64a² = 8 –4a²

a² = `2/17`