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

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

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=√((x_2-x_1)^2+(y_2-y_1)^2)`

This implies that;

`r=√((-2--5)^2+(1--3)^2)`

`r=√((-3)^2+(4)^2)`

`r=√(9+16)`

`r=√(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`