Question

Find the radius of a circle whose centre is $(-5,4)$ and which passes through the point $(-7,1)$.

Answer 1

We know that the distance between the two points $(x_1,y_1)$ and $(x_2,y_2)$ is

$d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Since, the radius of the circle is the distance between the centre and the point.

Let the centre of the circle is $)=(-5,4)$ and the point be $A=(-7,1)$, then the radius $OA$ is:

$OA=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}=\sqrt{{(-7+5)}^2+{(1-4)}^2}=\sqrt{{(-2)}^2+{(-3)}^2}=\sqrt{4+9}=\sqrt{13}$

Hence, the radius of the circle is $\sqrt{13}$ units.