Question

Find the equation of the circle which passes through the point of intersection of the lines 3x – 2y – 1 = 0 and 4x + y – 27 = 0 and whose centre is (2, – 3).

Answer 1

Let P be the point of intersection of the lines AB and LM whose equations are respectively 

3x – 2y – 1 = 0 ..........(i) 

and 4x + y – 27 = 0 ..........(ii) 

Solving (i) and (ii), we get x = 5, y = 7. So, coordinates of P are (5, 7). 

Let C(2, –3) be the centre of the circle. 

Since the circle passes through P, therefore

Hence the equation of the required circle is