From the point A 0 , 3 on the circle x 2 + 4 x + y − 3 2 = 0 , a chord A B is drawn and extended to a point M such that A M = 2 A B . The equation of the locus of M is:

Step-by-step solution

The equation of circle is, x 2 + y 2 + 4 x − 6 y + 9 = 0 ... 1 Given, A M = 2 A B ⇒ A B = M B Let the co-ordinates of M be h , k Then, B is mid point of A M and its coordinates are – B 0 + h 2 , 3 + k 2 or   B h 2 , k + 3 2 Now put B in eq. of circle To get h 2 4 + 2 h + k + 3 2 - 3 2 = 0 ⇒ h 2 + 8 h + k - 3 2 = 0 ⇒ h 2 + k 2 + 8 h - 6 k + 9 = 0