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

Question

Find the equation of the circle with:
Centre (a, b) and radius $\sqrt{\text{a}^2+\text{b}^2}$

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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)
$(\text{x}-\text{a})^2+(\text{y}-\text{b})^2=\big(\sqrt{\text{a}^2+\text{b}}\big)^2$
$\Rightarrow\text{x}^2-2\text{ax}+\text{a}^2+\text{y}^2-2\text{bx}+\text{b}^2=\text{a}^2+\text{b}^2$
$\Rightarrow\text{x}^2+\text{y}^2-2\text{ax}-2\text{by}=0$

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