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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.

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.

Grade:11

1 Answers

Shailendra Kumar Sharma
188 Points
6 years ago
(h,k) be point so Lenth of tangent to x2+y2 =a2 is \sqrt{h2+k2-a2}
and 
 x2+y2 =b2 is \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
 
 

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