Question

Find the equation of a circle which passes through the origin and makes intercepts $2$ units and $4$ units on $x$-axis and $y$-axis respectively.

• A. $x^{2} + y^{2} - 2x - 4y = 0$
• B. $x^{2} + y^{2} - 4y = 0$
• C. $x^{2} + y^{2} + 2x = 0$
• D. $x^{2} +y^{2} - 4x - 2y = 0$

Answer 1

Answer: (A)

As the circle passes through origin and makes intercepts $2$ units and $4$ units on $x$-axis and $y$-axis respectively, it passes through the points $A(2,0)$ and $B(0,4)$. Since axes are perpendicular to each other, therefore, $∠AOB=90^{\circ}$ and hence $AB$ becomes a diameter of the circle. So, the equation of the required circle is
$ (x - 2)(x - 0) + (y - 0) (y - 4) = 0$
or $x^{2} + y^{2} - 2x - 4y = 0$.