Question

A circle touches a given straight line and cutsoff a constant length $2d$ from another straight line perpendicular to the first straight line. The locus of the centre of the circle is

• A. hyperbola
• B. circle
• C. parabola
• D. Pair of perpendicular lines

Answer 1

The correct option is A hyperbola

let the equation of the circle $x^2+y^2+2gx+2fy+c=0$
It is touching x axis.The equation of the circle becomes
$x^2+2gx+c=0$
Since , it is touching x axis.D=0
$g^2=c$
Intercept made on y axis$=2\sqrt{f^2-c}$
$2\sqrt{f^2-c}=2d$
$f^2-c=d^2$
$f^2-g^2=d^2$
$y^2-x^2=d^2$