Answer:
The answer is the third one:
(x - 4)^2 + (y + 7)^2 = 53
Step-by-step explanation:
The equation for a circle is (x - h)^2 + (y - k) = r^2
(h, k) represents the center of the circle so that would be (4, -7)
now we already know this much of the equation: (x - 4)^2 + (y + 7)^2 = r^2
now to solve for r, radius, we take the other point we re given: (-3, -5)
Since the circle passes through point (-3, -5) and we know the center of the circle is (4, -7) then we know the distance between them is the radius
draw line on a graph from (-3, -5) to the center so we can get the side lengths and use the pythagorean theorem to solve for the length.
The side lengths will be 7 and 2 (find how many units from each other they are: -3 and 4 are 7 units apart. -5 and -7 are 2 units apart)
Now plug them in: a^2 + b^2 = c^2 (2)^2 + (7)^2 = c^2 4 + 49 = c^2
53 = c^2 now square root both sides to clear the square: √53 = √c^2 √52 = c
this is the length between the center and point (-3, -5) aka this is the radius: √53
in the equation for a circle we must square the radius, this clears the root so your answer is: (x - 4)^2 + (y + 7)^2 = (√53)^2 >>> (x - 4)^2 + (y + 7)^2 = 53
