Question

The locus of poles of chords of the circle $x^2+y^2=a^2$ subtending a right angle at the centre of the circle is a circle of radius equal to

• A. $2a$
• B. $a\sqrt{2}$
• C. $\frac{a}{2}$
• D. $\frac{a}{\sqrt{2}}$

Answer 1

The correct option is B $a\sqrt{2}$

Let AB is a chord of circle which substends right angle at origin
$\therefore P$ is pole of chord of AB

As $P$ is the center of the orthogonal circle with the given circle

Therefore $PAOB$ forms a square.
$\therefore OQ\cdot OP=a^2$
$OP\times \frac{a}{\sqrt{2}}=a^2$
$OP=\sqrt{2}a$
$\therefore (h-0{)}^2+(k-0{)}^2=2a^2$
$h^2+k^2=2a^2$
Hence locus of P(h,k) is
$x^2+y^2=2a^2$
$\Rightarrow$ radius of circle $=\sqrt{2}a$