Home
Class 11
MATHS
y=2x be a chord of the circle x^(2) +y^(...

`y=2x` be a chord of the circle `x^(2) +y^(2)=10x`. Find the equation of a circle whose diameter is this chord.

Text Solution

Verified by Experts

Put `y=2x` in the equation of circle `x^(2) +y^(2)=10x`
`x^(2)+(2x)^(2)-10x=0`
`rArr5x^(2)=10x=0`
`rArr5x(x-2)=0`
`rArr x=0 and x=2`
`rArr y=0 and y=4`
Therefore, the co-ordinates of the ends of chord `=(0,0) and (2,4)`
Now the equation of a circle taking `(0,0) and (2,4)` as the end points of a diameter
`(x-0)(x-2)+(y-0)(y-4)=0`
`rArrx^(2)-2x+y^(2)-4y=0`
`rArr x^(2) +y^(2)-2x -4y=0`.
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTION

    NAGEEN PRAKASHAN|Exercise Miscellaneous Example|3 Videos

  • CONIC SECTION

    NAGEEN PRAKASHAN|Exercise Exercise 11A|38 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN|Exercise MISCELLANEOUS EXERCISE|20 Videos

  • INTRODUCTION OF THREE DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|6 Videos

Similar Questions

Explore conceptually related problems

y=2x is a chord of the circle x^(2)+y^(2)-10x=0, then the equation of a circle with this chord as diameter is

If y=2x is a chord of the circle x^(2)+y^(2)-10x=0, find the equation of a circle with this chord as diameter.

If y=2x is the chord of the circle x^(2)+y^(2)-4x=0, find the equation of the circle with this chord as diameter.

y=mx is a chord of equation of circle x^(2)+y^(2)-2ax=0. Find the equation of circle this chord is diameter of a circle.

If y+3x=0 is the equation of a chord of the circle,x^(2)+y^(2)-30x=0, then the equation of the circle with this chord as diameter is:

The equation of a chord of the circle x^(2)+y^(2)+4x-6y=0 is given by x+2y=0. The equation of the circle described on this chord as diameter is

The equation of the circle whose diameter is common chord to the circles

A variable chord is drawn through the origin to the circle x^(2)+y^(2)-2ax=0. Find the locus of the center of the circle drawn on this chord as diameter.

From the origin,chords are drawn to the circle (x-1)^(2)+y^(2)=1. The equation of the locus of the mid-points of these chords is circle with radius

Chord of the circle x ^(2) +y ^(2) = 81 bisected at the point (-2,3) meets the diameter x + 5y =0 at a point