Question

Find the equation of the circle with centre $(-1,-2)$ and radius $5$

Answer 1

Since the centre of the circle is $(-1,-2)$ and its radius $5$

$\therefore$ the equation of the circle is ${(x-(-1))}^2+{(y-(-2))}^2=5^2$

$\Rightarrow {(x+1)}^2+{(y+2)}^2=25$

$\Rightarrow x^2+2x+1+y^2+4y+4-25=0$

$\Rightarrow x^2+y^2+2x+4y-20=0$