Question

The centre of the circle x = 3 + 5 cos θ, y = - 4 + 5 sin θ, is ______ 

Options

• (4, -3)

• (-4, 3)

• (3, -4)

• (-3, 4)

Answer 1

The centre of the circle x = 3 + 5 cos θ, y = - 4 + 5 sin θ, is (3, -4).

Explanation:

`(x - 3)/5 = costheta` ............(i)

and `(y + 4)/5 = sintheta` ...........(ii)

Squaring (i) and (ii) and adding, we get

`((x - 3)/5)^2 + ((y + 4)/5)^2 = 1`

⇒ (x - 3)² + (y + 4)² = 25

∴ Centre is (3, -4).