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. $\frac{1}{a}$
• C. $\sqrt{a}$
• D. $\frac{1}{\sqrt{a}}$

Answer 1

The correct option is B $\frac{1}{a}$

Because $hx+ky=1$ touches $x^2+y^2=a^2$, therefore $\left|\frac{-1}{\sqrt{h^2+k^2}}\right|=a$
$\Rightarrow h^2+k^2=\frac{1}{a^2}$
$\therefore$ Locus of (h, k) is $x^2+y^2=\frac{1}{a^2}$, which is a circle of radius $\frac{1}{a}.$