Question

if a point P is moving such that the lengths of tangent drawn from P to the circle x^2+y^2+8x+12y+15=0 and x^2+y^2-4x-6y-12=0 are equal then find the equation of the locus of P​

Answer 1

Step-by-step explanation:

Equations of the circles are 

S=x2+y2−4x−6y−12=0

S1=x2+y2+6x+18y+26=0

P(x1,y1) is any point on the locus and PT1, PT2 are the tangents from P to the two circles.

Given condition is

PT2PT1=32

3PT1=2PT2

3(x2+y2−4x−6y−12)=2(x2+y2+6x+18y+26)

3x2+3y2−12x−18y−36=2x2+2y2+12x+36y+52)

x2+y2−24

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