Question

Which equation represents a circle that contains the point (–5, –3) and has a center at (–2, 1)? Distance formula: (x – 1)2 + (y + 2)2 = 25 (x + 2)2 + (y – 1)2 = 5 (x + 2)2 + (y – 1)2 = 25 (x – 1)2 + (y + 2)2 = 5

Answer 1

Answer:

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

Step-by-step explanation:

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

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

Since the given circle contains the point (-5,-3) and it is centered at (-2,1), we can determine the radius of the circle using the distance formula;

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

This implies that;

$r=\sqrt{(-2--5)^2+(1--3)^2}$

$r=\sqrt{(-3)^2+(4)^2}$

$r=\sqrt{9+16}$

$r=\sqrt{25}$

$r=5$

We now substitute (h,k)=(-2,1) and r=5 into the formula to obtain;

$(x+2)^2+(y-1)^2=5^2$

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