Question

If 3x + y = 0 is a tangent to the circle with centre at the point (2, –1), then the equation of the other tangent to the circle from the origin is ______.

विकल्प

• x – 3y = 0

• x + 3y = 0

• 3x – y = 0

• 2x + y = 0

Answer 1

If 3x + y = 0 is a tangent to the circle with centre at the point (2, –1), then the equation of the other tangent to the circle from the origin is x – 3y = 0.

Explanation:

O is origin C(2, –1) centre

Let the required tangent is mx – y = 0

∴ OC is bisector of both tangents

⇒ `(m - (-1/2))/(1 + (-1/2)m) = (-1/2 - (-3))/(1 + (-1/2)(-3))` = 1

⇒ m = `1/3`

∴ x – 3y = 0 is required tangent