Question

If the line hx + ky = 1 touches `x^(2)+y^(2)=a^(2)`, then the locus of the point (h, k) is a circle of radius
A. a
B. 1/a
C. `sqrt(a)`
D. `1//sqrt(a)`

Answer 1

Correct Answer - B
It is given that the line `hx+ky=1` touches `x^(2)+y^(2)=a^(2)`.
`:. |(-1)/(sqrt(h^(2)+k^(2)))|=a rArr h^(2)+k^(2)=(1)/(a^(2))`
Hence, the locus of (h, k) is `x^(2)+y^(2)=1//a^(2)`, which is a circle of radius 1/a.