Question

Tangents are drawn from a point on the circle x² + y² = 25 to the ellipse 9x² + 16y² – 144 = 0 then find the angle between the tangents.

Options

• `π/4`

• `(3π)/4`

• `π/2`

• `(2π)/3`

Answer 1

`bb(π/2)`

Explanation:

Given equation of ellipse is 9x² + 16y² – 144 = 0

⇒ 9x² + 16y² = 144

⇒ `x^2/16 + y^2/9` = 1  ...(i)

Given equation of circle is x² + y² = 25 which is the director circle of the ellipse, therefore tangents drawn make angle `π/2`. Since drawn tangents are perpendicular to each other. So the angle between the tangents is `π/2`.