Question

​Question 10
10. Angle between the tangents drawn from point(4,5) to the ellipse x 2 16 + y 2 25 =1 is-
(A) π 3 ( B ) 5 π 6 ( C ) π 4 ( D ) π 2

Answer 1

Angle between the tangents is option (D) i.e π/2

The angle between two tangents of an ellipse x² / a² + y² / b² = 1, drawn from a point (x₀, y₀) is given by

tan(θ) = 2 {√a²y₀² + b²x₀² - a²b²} / (x₀² + y₀² - a² - b²)

Here, a²=16, b²=25, x₀=4, y₀=5

∴ the angle between the tangent is

tan(θ) = 2 {√16×25 + 25×16 − 16×25} / (16+25−16−25)

tan(θ) = ∞

⇒ (θ) = π / 2