Consider three circles x 2+y 2=1, x 2+y 2-8x+15=0,x 2+y 2​+10 y+24=0 .the point from which tangents of equal length can be drawn to all these three circles is____

Dear Student,

The point from which the 3 tangents to the given 3 circles are equal lies on the radical axis of 3 circles.Now given circles are S1x2+y2=1S2x2+y2-8x+15=0 and S3x2+y2+10y+24=0 Radical axis of S1 and S2 is given byS1-S2=0x2+y2-1-x2+y2-8x+15=0x2+y2-1-x2-y2+8x-15=0-1+8x-15=08x=16x=2radical axis of S2 and S3 is given by S2- S3=0x2+y2-8x+15-x2+y2+10y+24=0x2+y2-8x+15-x2-y2-10y-24=015-8x-10y-24=0putting x=215-24-8×2-10y=015-40=10y-25=10yy=-2510y=-52Hence the required point is 2,-52
Regards,

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