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# find the locus of a point which is such that the length of tangents from it to two concentric circles x^2+y^2=a^2 and x^2+y^2=b^2 vary inversely as their radii.

Shailendra Kumar Sharma
188 Points
3 years ago
(h,k) be point so Lenth of tangent to x2+y2 =ais $\sqrt{h2+k2-a2}$
and
x2+y2 =bis $\sqrt{h2+k2-b2}$
given
$\sqrt{h2+k2-b2}/\sqrt{h2+k2-a2} =\frac{a}{b}$
square both side

b2(h2+k2-b2) =a2(h2+k2-a20
(b2-a2)(h2+k2) =b4-a4
thus h2+k2=a2+b2
so x2+y2=a2+b2 is the locus