The equation of the circle passing through (0 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The circle passes through the origin $(0,0)$ and makes intercepts $a$ and $b$ on the $x$ and $y$ axes respectively.Therefore,the circle passes thr

Vedclass · Accepted Answer

$x^2+y^2-ax-by=0$

Vedclass · Answer

(D) The circle passes through the origin $(0,0)$ and makes intercepts $a$ and $b$ on the $x$ and $y$ axes respectively.Therefore,the circle passes through the points $(a,0)$ and $(0,b)$.Since the angle between the coordinate axes is $90^{\circ}$,the line segment joining $(a,0)$ and $(0,b)$ is a diameter of the circle.The equation of a circle with diameter endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by $(x-x_1)(x-x_2) + (y-y_1)(y-y_2) = 0$.Substituting $(x_1, y_1) = (a,0)$ and $(x_2, y_2) = (0,b)$:$(x-a)(x-0) + (y-0)(y-b) = 0$$x(x-a) + y(y-b) = 0$$x^2 - ax + y^2 - by = 0$$x^2 + y^2 - ax - by = 0$

The equation of the circle passing through $(0,0)$ and which makes intercepts $a$ and $b$ on the coordinate axes is

Similar Questions

Let the circles pass through the point $(-1, 1)$ and be tangent to the $x$-axis. If $(h, k)$ are the coordinates of the center of the circle,then the set of values of $k$ is given by which interval?

Let the equation $ax^2+2hxy+by^2+2gx+2fy+c=0$ represent a point circle other than the origin. Then which one of the following conditions must hold?

$A$ circle passes through $(-2, 4)$ and touches the $y-$axis at $(0, 2).$ Which one of the following equations can represent a diameter of this circle?

The equation of the circle with the origin as the centre passing through the vertices of an equilateral triangle whose median is of length $3a$ is

The equation of the circle of radius $3$ that lies in the fourth quadrant and touches the lines $x=0$ and $y=0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module