Question

A line is at a distance ${}^{\prime }{c}^{\prime }$ from origin and meets axes in $A$ and $B$. the locus of the centre of the circle passing through $O,A$ is

• A. $x^2+y^2=c^2$
• B. $x^2+y^2=2c^{-2}$
• C. $x^2+y^2=3c^{-2}$
• D. $x^2+y^2=4c^{-2}$

Answer 1

The correct option is A $x^2+y^2=c^2$

Given that,

Let a line OM is at distance ‘c’ from origin and meets axes in A and B.

let O be the origin and point of $C(h,k)$.

The points A and B are meets both axes then points of $A(0,2k)$ and $B(2h,0)$ and points of $M(h,k)$

Then,

$OM=c$

$\sqrt{{(h-0)}^2+{(k-0)}^2}=c$

Squaring both side and we get,

$h^2+k^2=c^2$

Hence the locus of this equation

$x^2+y^2=c^2$

Hence it is correct answer.