Question

From the point $A(0.3)$ on the circle $x^2+4 x+(y-3)^2=0$ a chord $A B$ is drawn \& extended to a point $M$ such that $A M=2 A B$. The equation of the locus of $M$ is :

• A. $x^2+8 x+y^2=0$
• B. $ x^2+8 x+(y-3)^2=0$
• C. $(x-3)^2+8 x+y^2=0$
• D. $x^2+8 x+8 y^2=0$

Answer 1

Answer: (B)

B lies on circle
$\left(\frac{ h }{2}\right)^2+4\left(\frac{ h }{2}\right)+\left(\frac{ k +3}{2}-3\right)^2=0 $
$\Rightarrow \frac{ h ^2}{4}+2 h +\frac{( k -3)^2}{4}=0$
Hence locus of $(h, k) x^2+8 x+(y-3)^2=0$