Find the equation of the circle with: Centre (a , a ) and radius … - Vidyadip

Question

Find the equation of the circle with:
Centre $(\text{a}\cos\alpha,\ \text{a}\sin\alpha)$ and radius a.

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Answer

The general equation of circle is $(\text{x}-\text{a})^2+(\text{y}-\text{b})^2=\text{r}^2\ .....(\text{A})$
where(a, b)are centre and r is radius
From (A)
$(\text{x}-\text{a}\cos\alpha)^2+(\text{y}-\text{a}\sin\alpha)^2=\text{a}^2$
$\Rightarrow\text{x}^2-2\text{a}\cos\alpha\text{x}-2\text{a}\sin\alpha\ \text{y}=0$

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