Home
Class 12
MATHS
The locus of the centre of the circle wh...

The locus of the centre of the circle which bisects the circumferences of the circles `x^2 + y^2 = 4 & x^2 + y^2-2x + 6y + 1 =0` is :

A

`2x - 6y - 15 = 0`

B

`2x +6y +15 = 0`

C

`2x - 6y +15 = 0`

D

`2x +6y - 15 = 0`

Text Solution

Verified by Experts

The correct Answer is:
A
Let required circle be `x^(2) + y^(2) + 2gx +2fy +c =0`.
Hence, common chord with `x^(2) + y^(2) -4 =0` is
`2gx +2fy +c +4 =0`
This is diameter of circle `x^(2) + y^(2) =4` hence `c =-1.` Now, again common chord with other circle is:
`2x(g+1) + 2y (f-3) +(c-1) =0`
This is diameter of `x^(2) + y^(2) -2x +6y +1 =0`.
`:. 2(g+1) -6 (f-3) -5 =0`
or `2g - 6f +15 =0`
Locus is `2x -6y -15 =0`, which is straight line.
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|9 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise For problems 3 and 4|2 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

Similar Questions

Explore conceptually related problems

The locus of the centre of the circle of radius 2 which rolls on the inside of the circle x^2+y^2+3x-6y-9=0 is

The locus of the centre of a circle radius 2 which rolls on the outside of the circle x^2+y^2+3x-6y-9=0 is

Find the equation of the circle which bisects the circumference of the circle x^(2) + y^(2) + 2y - 3 = 0 and touches the straight line y = x at the origin.

The locus of the centre of the circle which cuts orthogonally the circle x^2+y^2-20x+4=0 and which touches x=2 is :

Center of the circle x^(2) + y^(2) - 4x + 6y - 12 = 0 is -

If the circle x^2+y^2+6x+8y+a=0 bisects the circumference of the circle x^2 + y^2 + 2x - 6y - b = 0 then (a + b) is equal to

Center of the circle x^(2) + y^(2) - 6x + 4y - 12 = 0 is -

The locus of the centre of a circle which touches externally the circle x^2 + y^2-6x-6y+14 = 0 and also touches Y-axis, is given by the equation (a) x^2-6x-10y+14 = 0 (b) x^2-10x-6y + 14 = 0 (c) y^ 2-6x-10y+14-0 (d) y^2-10x-6y + 14 = 0

The equation of the circle whose diameter is the common chord of the circles x^2+y^2+3x+2y+1=0 and x^2+y^2+3x+4y+2=0 is

What is the equation to the locus of the centre of a circel of radius 1 unit which rolls inside the circle x ^(2) +y^(2) -2x +2y -7 =0 ?