Question

find the equation of the circle if the chords of the circle joining (1,2) and (-3,1) subtends 90° at the centre of the circle .

Answer 1

Solution :- The chord joining points A ( 1,2) and B ( -3,1) subtends 90° at the centre of the circle . then AB subtends an angle 45° at point X on the circumference . therefore , the equation of the circle is

(x - 1) ( x + 3) + ( y - 2) ( y - 1)

= +- cot45° [(y-2)(x+3) -(x -1( (y-1)]

or, x² + y² + 2x - 3y - 1 = +-[4y-x-7]

or, x² + y² + 3x & 7y + 6 = 0

and, x² + y² + x + y - 8 = 0