Question

Find the equation of the circle with:

Centre (a cos α, a sin α) and radius a.

Answer 1

 Here, h = \[a\cos\alpha\] , k = \[a\cos\alpha\]

\[a\cos\alpha\]  and radius = a

∴ Required equation of the circle:

\[\left( x - a\cos\alpha \right)^2 + \left( y - a\sin\alpha \right)^2 = \left( a \right)^2\]

\[\Rightarrow x^2 + a^2 \cos^2 \alpha - 2ax\cos\alpha + y^2 + a^2 \sin^2 \alpha - 2ay\sin\alpha = a^2 \]

\[ \Rightarrow x^2 + a^2 \left( \sin^2 \alpha + \cos^2 \alpha \right) - 2ax\cos\alpha + y^2 - 2ay\sin\alpha = a^2 \]

\[ \Rightarrow x^2 + a^2 - 2ax\cos\alpha + y^2 - 2ay\sin\alpha = a^2 \]

\[ \Rightarrow x^2 + y^2 - 2ax\cos\alpha - 2ay\sin\alpha = 0\]