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.

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) x2 + y2 - 2x - 4y = 0 (B) x2 + y2 - 4y = 0 (C) x2 + y2 + 2x = 0 (D) x2 +y2 - 4x - 2y = 0

Tardigrade Admin · Accepted Answer

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,

∠ A OB = 9 0^{\circ}

and hence

A B

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} - 2 x - 4 y = 0

.

Q. 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.

$x^{2} + y^{2} - 2 x - 4 y = 0$

$x^{2} + y^{2} - 4 y = 0$

$x^{2} + y^{2} + 2 x = 0$

$x^{2} + y^{2} - 4 x - 2 y = 0$

Q. 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.

x2+y2−2x−4y=0

x2+y2−4y=0

x2+y2+2x=0

x2+y2−4x−2y=0

Q. 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.

$x^{2} + y^{2} - 2 x - 4 y = 0$

$x^{2} + y^{2} - 4 y = 0$

$x^{2} + y^{2} + 2 x = 0$

$x^{2} + y^{2} - 4 x - 2 y = 0$