Question

if the centre of a circle is (2a,a-7) then find value of a,if circle passes through the point(11,-9) and has diameter 10(root)2 units.

Answer 1

Centre of circle = (2a - 1, a) Point on circle = (10, -2) Diameter = 10√2 units Hence radius = 5√2 units That is distance between (2a -1 a) and (10, -2) = 5√2 units √[(10 - 2a + 1)2 + (-2 - a)2] = 5√2 Squaring on both the sides, we get (9 - 2a)2 + (-2 - a)2 = 50 5a2 - 32a + 35 = 0 5a2 - 25a - 7a + 35 = 0 5a(a - 5) - 7(a - 5) = 0 (a -5)(5a - 7) = 0 Hence a = 5 or 7/5