Objective question in Circle

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The locus of the centre of circle which cuts the circles {{x}^{2}}+{{y}^{2}}+4x-6y+9=0 and {{x}^{2}}+{{y}^{2}}-4x+6y+4=0 orthogonally is

#Mathematics #Co-ordinate Geometry #Circle

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Shahrukh Uddin ·2012-09-30 23:25:59

let the centre be (h,k)
h=-g k=-f
g=-h f=-k ------(1)
now if it intersects orthogonally then from theformula,4g-6f=c=9 and -4g+6f=c+4 then eliminating c we get
8g-12f=5
substituting (1),we get
12k-8h=5
=>8h-12k+5=0
now h=x and k=y
8x-12y+5=0 is the locus of the centre of the circle.but answer went wrong in chakravyuh test please tell where i went wrong.

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Shahrukh Uddin ·2012-09-30 23:27:22

answer given there is 12x+8y+5=0

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Objective question in Circle

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