Question

Answer the following :

Find the equation of the tangent to Circle x = 5 cosθ. y = 5 sinθ, at the point θ = `pi/3` on it

Answer 1

The equation of a tangent to the circle

x² + y² = r² at P(θ) is

x cosθ + y sinθ = r

Here, r = 5, θ = `pi/3`

∴ the equation of the tangent at P`(pi/3)` is

`x cos  pi/3 + y sin  pi/3` = 5

∴ `x(1/2) + y(sqrt(3)/2)` = 5

∴ `x + sqrt(3)y` = 10