**Parametric equation of a circle worksheet :**

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

(1) Find the parametric equations of the circle x^{2} + y^{2} = 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 4x^{2} + 4y^{2} = 9

**Question 1 :**

Find the parametric equations of the circle x^{2} + y^{2} = 16

**Solution :**

Here r^{2} = 16 ⇒ r = 4

The parametric equations of the circle

x^{2} + y^{2} = r^{2} in parameter θ are x = r cosθ, y = r sin θ

The parametric equations of the given circle x^{2} + y^{2} = 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

cos^{2}θ + sin^{2}θ = 1

(x/2)^{2} + (y/2)^{2} = 1

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

cos^{2}θ + sin^{2}θ = 1

(4x)^{2} + (4y)^{2} = 1

16x^{2} + 16y^{2} = 1

16x^{2} + 16y^{2} = 1 is the required cartesian equation of the circle.

**Question 4 :**

Find the parametric equation of the circle 4x^{2} + 4y^{2} = 9

**Solution :**

4x^{2} + 4y^{2} = 9

Divide the equation by 4

x^{2} + y^{2} = (9/4)

Here r^{2} = 9/4 ⇒ r = 3/2

The parametric equations of the circle x^{2} + y^{2} = r^{2} 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

- How to find the length of tangent
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- Inside outside or on the circle

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