Question

The equation of the circle which passes through the origin and makes intercepts of length a and b on the x and y axes respectively, are

• A. $x^2+y^2\pm ax\pm by=0$
• B. $x^2\pm y^2=0$
• C. $x^2\pm ax\pm by=0$
• D. $Noneofthese$

Answer 1

The correct option is A $x^2+y^2\pm ax\pm by=0$

General equation of circle $x^2+y^2=2gx+2fy+c=0$

$\because$ it passes through origin

it cuts an intercept $(0,0)$ and $(0,b)$ on $X$ and $Y$ area respectively

by putting $(a,0)$ we get $A^2+2ga=0$

$\Rightarrow$ $a=-2g$

by putting $(0,b)$ we get $b^2+2fb=0$

$\Rightarrow$ $b=-2f$

$\therefore$ Equation of circle $=x^2+y^2-ax-by=0$