Find the equations of the following curves in cartesian form. Also find the centre and radius of the circle $x = a + c cos θ, y = b + c sin θ$

Open in App

Solution

We have $x = a + c cos θ, y = b + c sin θ$
$\Rightarrow cos θ = \frac{x - a}{c}, sin θ = \frac{y - b}{c}$
$\Rightarrow {(\frac{x - a}{c})}^{2} + {(\frac{y - b}{c})}^{2} = {cos}^{2} θ + {sin}^{2} θ \Rightarrow {(x - a)}^{2} + {(y - b)}^{2} = c^{2}$
Clearly it is a circle with centre at (a, b) and radius c

Suggest Corrections

Similar questions

x = a + r cos α, y = b + r sin α

x = - 1 + 2 sin θ, y = 1 + 2 cos θ .

x = - 1 + 2 cos a, y = 3 + 2 sin a

(0 ⩽ a < 2 π)

x = 5 cos θ, y = 5 sin θ

x = 2 + 3 cos θ, y = 3 - 3 sin θ

x = a sin θ + c cos θ

y = a cos θ - c sin θ

x^{2} + y^{2} = a^{2} + c^{2}

Join BYJU'S Learning Program