Home
Class 11
MATHS
Find the equation of a circle which pass...

Find the equation of a circle which passes the centre of the circle `x^(2)+y^(2)-6x =1` and concentric with the circle `2x^(2)+2y^(2)-8x +12y -1=0`.

Text Solution

Verified by Experts

`x^(2)+y^(2)-6x=1`
`rArrx^(2)+y^(2)-6x-1=0`
Here `2g=-6 and 2f=0`
`rArr g =-3 and f=0`
Centre `=(-g,-f)=(3,0)`
Equation of second circle
`2x^(2)+2x^(2)-8x+12y-1=0`
`rArrx^(2)+y^(2)-4x+6y-(1)/(2)=0`
Let the equation of concentric circle be
`x^(2)+y^(2)-4x +6y +c=0` ....(1)
The circle passes through the point (3, 0)
`:. 9+0-12 +0+c=0`
`rArr c=3`
Put c = 3 in eq. (1)
`x^(2)+y^(2) -4x+6y +3=0`
which is the required equation.
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

Find the equation of the circle passing through the centre of the circle x^(2)+y^(2)+8x+10y-7=0 and concentric with the circle x^(2)+y^(2)-4x-6y=0

(i) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 6x + 12y + 15 = 0 and of double its radius. (ii) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 2x - 4y + 1 = 0 and whose radius is 5. (iii) Find the equation of the cricle concentric with x^(2) + y^(2) - 4x - 6y - 3 = 0 and which touches the y-axis. (iv) find the equation of a circle passing through the centre of the circle x^(2) + y^(2) + 8x + 10y - 7 = 0 and concentric with the circle 2x^(2) + 2y^(2) - 8x - 12y - 9 = 0 . (v) Find the equation of the circle concentric with the circle x^(2) + y^(2) + 4x - 8y - 6 = 0 and having radius double of its radius.

Find the equation of the circle which passes through the centre of the circle x^2 + y^2 + 8x + 10y-7 = 0 and is concentric with the circle 2x^2 + 2y^2 - 8x - 12y - 9=0

Find the equation of the circle passing through the centre of the circle x^2 +y^2 -4x-6y=8 and being concentric with the circle x^2 +y^2 - 2x-8y=5 .

Equation of circle passing through the centre of the circle x^(2)+y^(2)-4x-6y-8=0 and being concentric with the circle x^(2)+y^(2)-2x-8y-5=0 is

Find the equation of a circle which passes through the point (3, 2) and concentric with the circle x^(2)+y^(2)-4x +2y - 1=0 .

Find the equation of the circle concentric with the circle 2x^(2)+2y^(2)-8x+10y-39=0

Find the equation of the circle passing through (-2,14) and concentric with the circle x^(2)+y^(2)-6x-4y-12=0