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The locus of a point such that the tangents drawn from it to the circle x2 + y2 - 6x - 8y = 0 are perpendicular to each other is

The locus of a point such that the tangents drawn from it to the circle x2 + y2 - 6x - 8y = 0 are perpendicular to each other is

Grade:11

1 Answers

Sunil Raikwar
askIITians Faculty 45 Points
8 years ago
Let the required point be (h,k) then the equation of pair of tangents draw from it to the circle
ss1=t2 or( x2+y2-6x-8y)(h2+k2-6h-8k)=(hx+ky-3(x+h)-4(y+K))2, if tangents are perpendicular then sum of coefficient of x2 & y2equal to zero.
h2+k2-(h-3)2+h2+k2-(k-4)2=0
by solving it we get the required locus of (h,k)

Thanks & Regards
Sunil Raikwar
askIITians Faculty


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