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 = r²

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 = 5²

(x + 2)² + (y - 1)² = 5²

Therefore, the equation of the circle is (x + 2)² + (y - 1)² = 5².

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 = 5².