Maharashtra State BoardHSC Science (Electronics) 11th
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Write the parametric equations of the circle: (x − 3)2 + (y + 4)2 = 25 - Mathematics and Statistics

Sum

Write the parametric equations of the circle:

(x − 3)2 + (y + 4)2 = 25

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Solution 1

The equation of the circle is

(x − 3)2 + (y + 4)2 = 25

Comparing this equation with (x – h)2 + (y – k)2 = r2,

we get, h = 3, k = – 4 and r = 5

∴ the parametric representation of the circle is

x = h + r cos θ, y = k + r sin θ

i.e., x = 3 + 5 cos θ, y = – 4 + 5 sin θ.

Solution 2

The equation of the circle is

(x − 3)2 + (y + 4)2 = 25

Comparing this equation with (x – h)2 + (y – k)2 = r2,

we get, h = 3, k = – 4 and r = 5

∴ the parametric representation of the circle is

x = h + r cos θ, y = k + r sin θ

i.e., x = 3 + 5 cos θ, y = – 4 + 5 sin θ.

Concept: Parametric Form of a Circle
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