which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?\ndistance…

which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?\ndistance formula: $sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$\n$(x - 1)^2+(y + 2)^2 = 25$\n$(x + 2)^2+(y - 1)^2 = 5$\n$(x + 2)^2+(y - 1)^2 = 25$\n$(x - 1)^2+(y + 2)^2 = 5$

which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?\ndistance formula: $sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$\n$(x - 1)^2+(y + 2)^2 = 25$\n$(x + 2)^2+(y - 1)^2 = 5$\n$(x + 2)^2+(y - 1)^2 = 25$\n$(x - 1)^2+(y + 2)^2 = 5$

Answer

Explanation:

Step1: Calculate the radius

The distance between the center $(-2,1)$ and the point $(-5,-3)$ on the circle is the radius $r$. Using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, where $(x_1,y_1)=(-2,1)$ and $(x_2,y_2)=(-5,-3)$. $r=\sqrt{(-5 + 2)^2+(-3 - 1)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Step2: Write the equation of the circle

The standard - form of the equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle. Here, $h=-2,k = 1,r = 5$. So the equation is $(x+2)^2+(y - 1)^2=25$.

Answer:

C. $(x + 2)^2+(y - 1)^2=25$