Home
Class 12
MATHS
Find the equation of circles determined ...

Find the equation of circles determined by the following conditions. Circle passes through origin and cuts off intercepts a and b from the axes.

Text Solution

Verified by Experts

Let the equation of the circle be
`x^2+y^2+2gx+2fy+c=0`
As it passes through the points (a, 0) and (0, 0).
We have c = 0, `a^2 + 2gs = 0`, `b^2 + 2fb = 0`
`therefore` 2g = -a, 2f = -b.
`therefore` Equation of the circle is `x^2 + y^2 -ax - by = 0`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    MBD PUBLICATION|Exercise QUESTION BANK|76 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MBD PUBLICATION|Exercise QUESTION TYPE|4 Videos

Similar Questions

Explore conceptually related problems

Find the equation of circles determined by the following conditions.The centre at (-2, 3) and passing through origin.

Find the equation of circles determined by the following conditions. Circle touches the axis of x at a distance 3 from origin and intercepts a distance of 6 on the y-axis.

Find the equation of circles determined by the following conditions. The ends of diameter are (-5, 3) and (7, 5).

Find the equation of circles determined by the following conditions. Circle is tangent to x-axis and passes through (1, -2) and (3, -4)

Find the equation of circles determined by the following conditions. The centre at (1, 4) and passing through (-2, 1).

Find the equation of circles determined by the following conditions.The centre is on the x-axes and the circle passes through the origin and the point (4, 2).

Find the equation of circles determined by the following conditions. The radius is 5 and circle is tangent to both axes.

Find the equation of circles determined by the following conditions. The centre at (-1, 4) and circle tangent to y-axis.

Find the equation of circles determined by the following conditions. The centre at (3, 2) and circle is tangent to x-axis.

Find the equation of circles determined by the following conditions. The circle touches the axis of x at (3, 0) and also touches the line 3y - 4x =12.

Home
Profile