Question

(i) Find the equation of tangent of the circle x² + y² = 64 which passes through point (4, 7).

(ii) Find the equation of tangent of the circle x² + y² – 4 which makes an angle of 60° with x-axis.

Answer 1

(i) Equation of circle

x² – y² = 64

⇒ x² + y² = (8)²

Equation of tangent passing through (4, 7)

(y – y₁) = m(x – x₁)

⇒ (y – 7) = m(x – 4)

⇒ y – 7 = mx – 4m

⇒ mx – y – 4m + 7 = 0 …(i)

∵ line of Eq. (i) touches the circle

∴ Perpendicular drawn from centre (0, 0) of circle to the tangent will be equal to radius of circle,

(ii) Equation of circle,