Question

A circle is centered at D(-1,3)D(−1,3)D, left parenthesis, minus, 1, comma, 3, right parenthesis. The point G(-10,1)G(−10,1)G, left parenthesis, minus, 10, comma, 1, right parenthesis is on the circle.

Answer 1

We have been given that a circle is centered at D(-1,3). The point G(-10,1) is on the circle. We are asked to write the equation of circle.

We know that standard equation of a circle is $(x-h)^2+(y-k)^2=r^2$, with center at point (h,k) and radius r.

First of all we will find radius of circle using distance formula.

$r=\sqrt{(-10+1)^2+(1-3)^2}$

$r=\sqrt{(-9)^2+(-2)^2}$

$r=\sqrt{81+4}$

$r=\sqrt{85}$

Now we will substitute coordinates of center and radius in equation of circle.

$(x-(-1))^2+(y-3)^2=\left(\sqrt{85}\right )^2$

$(x+1)^2+(y-3)^2=85$

Therefore, the equation of circle would be $(x+1)^2+(y-3)^2=85$.