Question

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

Distance formule: (x2 - x1)2 +(y2-y1)2
(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 centre is at (-2, 1) so the equation is:

(x + 2)^2 + (y - 1)^2 = r^2 where r is the radius.

The radius is the distance from the centre to the point (-5, -3).

Using the distance formula:

r = √ [(-3- 1)^2 + (-5 - -2)^2]

and r^2 = (-3- 1)^2 + (-5 - -2)^2

= (-4)^2 + (-3)^2

= 16 + 9

= 25.