The equation of the circle which passes through the points (2, 3) and (4, 5) and whose centre lies on a straight line 4x - y - 3 = 0 , is

Step-by-step solution

Let the centre of the circle be (h, k) . Since the centre lies on the line 4x - y - 3 = 0 , we have 4h - k - 3 = 0 k = 4h - 3 . The circle passes through the points (2, 3) and (4, 5) , so the distance from the centre to both points is equal to the radius r . (h - 2)^2 + (k - 3)^2 = (h - 4)^2 + (k - 5)^2 -4h + 4 - 6k + 9 = -8h + 16 - 10k + 25 4h + 4k = 28 h + k = 7 Substituting k = 4h - 3 into the above equation: h + 4h - 3 = 7 5h = 10 h = 2 Then k = 4(2) - 3 = 5 . The centre of the circle is (2, 5) . The radius squ