= ab +y)+cbx+y)=0 * 5. From the point A(0,3) on the circle x2 + 4x +(y-3)2 = 0, a chord AB drawn and extended to a point M such that AM=2AB. Find the equation of the locus of M.

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Let us assume this point ( m ) to have 60 - ondinaks ( (h, k) ) now, it is qiven that ( A M=2 A B ) Which means mid-point of Am is foint is which lies on the circle [ text { So, point } B Rightarrowleft(frac{h}{2}, frac{k+3}{2}right) ] This point lies on the circle &o it must &atify ) ts eq ( ^{n} ) ( Rightarrowleft(frac{h}{2}right)^{2}+4left(frac{h}{2}right)+left(frac{k+3}{2}-3right)^{2}=0 ) ( Rightarrow frac{b^{2}+2 h+left(frac{k-3}{4}right)^{2}}{4}=0 Rightarrow frac{h^{2}+k^{2}}{4}+2 h-frac{6 k}{4}+frac{9}{4}=0 ) [ Rightarrow h^{2}+k^{2}+8 h-6 k+9=0 ] New, leplace (hik) ley (x,y) So, locus of point m is ( x^{2}+y^{2}+8 x-6 y+9=0 )

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