Question

what is the standard form of the equation of a circle with its center at (2,-3) and passing through the point (-2,0)?

Answer 1

The standard equation of the circle is given by:
 (x-h) ^ 2 + (y-k) ^ 2 = r ^ 2
 Where,
 h, k: coordinates of the center of the circle
 r: radius of the circle.
 We are looking for the radio now:
 (-2-2) ^ 2 + (0 + 3) ^ 2 = r ^ 2
 (-4) ^ 2 + (3) ^ 2 = r ^ 2
 16 + 9 = r ^ 2
 25 = r ^ 2
 5 = r
 Substituting:
 (x-2) ^ 2 + (y + 3) ^ 2 = 5 ^ 2
 (x-2) ^ 2 + (y + 3) ^ 2 = 25
 Answer:
 The standard form of the equation of a circle is:
 (x-2) ^ 2 + (y + 3) ^ 2 = 25