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From the point A(0,3) on the circle x^2 + 4x + (y-3)^2 =0 a chord AB is drawn & extended to a point M such that AM=2AB . The equation of the locus of m will be?

From the point A(0,3) on the circle x^2 + 4x + (y-3)^2 =0 a chord AB is drawn & extended to a point M such that AM=2AB . The equation of the locus of m will be?

Grade:11

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
5 years ago
This is the equation of given circle
x^2 + 4x + (y-3)^2 =0
x^2 + 4x +4 + (y-3)^2 =4
(x+2)^2+ (y-3)^2 =4
So, centre is (-2,3) and radius = 2

Now Let M(h,k)
AM=2AB

Now B is the midpoint of A and M
SoB(\frac{h}{2},\frac{k+3}{2})

Now we know that
AM^2=4AB^2
apply this condition and you will get the ans

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