## About "Parametric equation of a circle worksheet"

Parametric equation of a circle worksheet :

Here we are going to see some practice questions on finding parametric equation of circle.

## Parametric equation of a circle worksheet - Practice questions

(1)  Find the parametric equations of the circle x2 + y2 = 16

(2)  Find the cartesian equation of the circle whose parametric equations are x = 2 cos θ, y = 2 sin θ, 0 ≤ θ ≤ 2π

(3)  Find the cartesian equation of the circle whose parametric equations are x = 1/4 cosθ, y = 1/4 sin θ and 0 ≤ θ ≤ 2π

(4)  Find the parametric equation of the circle 4x2 + 4y2 = 9

## Parametric equation of a circle worksheet - Solution

Question 1 :

Find the parametric equations of the circle x2 + y2 = 16

Solution :

Here r2 = 16 ⇒ r = 4

The parametric equations of the circle

x2 + y2 = r2 in parameter θ are x = r cosθ, y = r sin θ

The parametric equations of the given circle x2 + y2 = 16 are

x = 4 cos θ, y = 4 sin θ and 0 ≤ θ ≤ 2π

Question 2 :

Find the cartesian equation of the circle whose parametric equations are x = 2 cos θ, y = 2 sin θ, 0 ≤ θ ≤ 2π

Solution :

To find the caretsian equation of the circle, eliminate the parameter ‘θ’ from the given equations,

cos θ = x/2 ; sin θ = y/2

cos2θ + sin2θ  =  1

(x/2)2 + (y/2)2  =  1

x2 + y2 = 4 is the required cartesian equation of the circle.

Question 3 :

Find the cartesian equation of the circle whose parametric equations are x = 1/4 cosθ, y = 1/4 sin θ and 0 ≤ θ ≤ 2π

Solution :

To find the caretsian equation of the circle, eliminate the parameter ‘θ’ from the given equations,

x = (1/4) cosθ ; y = (1/4) sin θ

cosθ = 4x, sinθ = 4y

cos2θ + sin2θ  =  1

(4x)2 + (4y)2  =  1

16x2 + 16y2  =  1

16x2 + 16y2  =  1 is the required cartesian equation of the circle.

Question 4 :

Find the parametric equation of the circle 4x2 + 4y2 = 9

Solution :

4x2 + 4y2 = 9

Divide the equation by 4

x2 + y2 = (9/4)

Here r2 = 9/4 ⇒ r = 3/2

The parametric equations of the circle x2 + y2 = r2 in parameter θ are x = r cosθ, y = r sin θ

The parametric equations of the given circle

x = (3/2) cos θ, y = (3/2) sin θ and 0 ≤ θ ≤ 2π

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