# Which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?

**Solution:**

The equation of a circle with center (h, k) and radius r is

(x - h)^{2} + (y - k)^{2} = r^{2}

It is given that

Center = (-2, 1)

Point = (-5, -3)

The formula of distance is

\( \\d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} \\ \\ r = \sqrt{[(-5)-(-2)]^{2}+[(-3)-1]^{2}} \\ \\r=\sqrt{[-3]^{2}+[-4^{2}]} \\ \\r=\sqrt{9+16}\)

r = √25

r = 5

Substituting the values in the equation

(x - (-2))^{2} + (y - 1)^{2} = 5^{2}

(x + 2)^{2} + (y - 1)^{2} = 5^{2}

Therefore, the equation of the circle is (x + 2)^{2} + (y - 1)^{2} = 5^{2}.

## Which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?

**Summary:**

The equation which represents a circle that contains the point (-5, -3) and has a center at (-2, 1) is (x + 2)^{2} + (y - 1)^{2} = 5^{2}.