Question

The equations of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the x and y-axes respectively are

• A. $x^2+y^2\pm 4x\pm 8y=0$
• B. $x^2+y^2\pm 2x\pm 4y=0$
• C. $x^2+y^2\pm 8x\pm 16y=0$
• D. $x^2+y^2\pm x\pm y=0$

Answer 1

The correct option is A $x^2+y^2\pm 4x\pm 8y=0$

Let $S=x^2+y^{2}0+2gx+2fy=0$ be the equation of circle which passes through origin

$C=(-g,-f),r=\sqrt{g^2+f^2}$

Given that it makes intercept of 4 with x-axis

$⟹4=2\sqrt{r^2–d^2}$

Where d is distance between center and chord

$⟹2=\sqrt{g^2+f^2–f^2}$

$g=\pm 2$

Similarly

$⟹2=\sqrt{g^2+f^2–g^2}$

$g=\pm 4$

Equation of circle is

$x^2+y^2\pm 4x\pm 8y=0$