Question

Write the standard equation of a circle that passes through (1, −6) with center (7, −2).

Answer 1

The standard equation of the circumference is given by:
 (x ─ a) ^ 2 + (and ─ b) ^ 2 = r ^ 2
 Where,
 The ordered pair (a, b) represents the center of the circle.
 The radius of the circumference is r.
 In this case to find the radius of the circumference we must find the distance between the points (1, -6) and (7, -2).
 We have then:
 r = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
 r = root ((7-1) ^ 2 + (-2 - (- 6)) ^ 2)
 r = 2 * root (13)
 The equation of the circumference will be:
 (x ─ 7) ^ 2 + (y + 2) ^ 2 = (2 * root (13)) ^ 2
 (x ─ 7) ^ 2 + (y + 2) ^ 2 = 52
 Answer:
 (x ─ 7) ^ 2 + (y + 2) ^ 2 = 52