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प्रश्न
Find the equation of the circle with:
Centre (a cos α, a sin α) and radius a.
उत्तर
Here, h = \[a\cos\alpha\] , k = \[a\cos\alpha\]
\[\Rightarrow x^2 + a^2 \cos^2 \alpha - 2ax\cos\alpha + y^2 + a^2 \sin^2 \alpha - 2ay\sin\alpha = a^2 \]
\[ \Rightarrow x^2 + a^2 \left( \sin^2 \alpha + \cos^2 \alpha \right) - 2ax\cos\alpha + y^2 - 2ay\sin\alpha = a^2 \]
\[ \Rightarrow x^2 + a^2 - 2ax\cos\alpha + y^2 - 2ay\sin\alpha = a^2 \]
\[ \Rightarrow x^2 + y^2 - 2ax\cos\alpha - 2ay\sin\alpha = 0\]
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