Question

If a chord of the circle $x^2+y^2=a^2$ makes an angle 2$\alpha$ at the origin then the locus of the pole of that chord with respect to the circle $x^2+y^2=a^2$ is the circle whose radius is

• A. a $\sec \alpha$
• B. $a^2{\sec }^2\alpha$
• C. a $\tan \alpha$
• D. $a$ cosec $\alpha$

Answer 1

The correct option is A a $\sec \alpha$

$P(h,k)$ is a pole of chord $AB$
$\Rightarrow OQ=acosx$
$OP\cdot OQ=a^2$
$OP=asecx$
$\therefore (h-0{)}^2+(k-0{)}^2=(asecx{)}^2$
$\therefore h^2+k^2=a^{2}se{c}^{2}x$