Home
Class 12
MATHS
If the circle x^2+y^2+2a1x+c=0 lies comp...

If the circle `x^2+y^2+2a_1x+c=0` lies completely inside the circle `x^2+y^2+2a_2x+c=0`, then

A

`a_(1)a_(2) gt 0`, `clt0`

B

`a_(2)a_(2) lt 0`, `clt0`

C

`a_(1)a_(2) gt 0`, `cgt0`

D

`a_(1)a_(2) gt 0`, `clt0`

Text Solution

Verified by Experts

The correct Answer is:
C
The equation of radical axis of the given circle is `x=0`
If one circle lies completely inside the other, the centers of both circles should lie on the same side of the radical axis and the radical axis shouls not intersect the circles. Therefore,
`( -a_(1))(-a_(2))=0`
or `a_(1)a_(20 gt 0`
Also, `y^(2)+c=0` should have imaginary roots, ie., `c gt0`
Promotional Banner

Similar Questions

Explore conceptually related problems

If the circle x^(2)+y^(2)+2a_(1)x+c=0 lies completely inside the circle x^(2)+y^(2)+2a_(2)x+c=0 then

If the origin lies inside the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 , then

If the circle x^(2) + y^(2) = 9 touches the circle x^(2) + y^(2) + 6y + c = 0 internally, then c is equal to

The area of the portion of the circle x^(2)+y^(2)=1 which lies inside the parabola y^(2)=1-x, is -

If the circle x^(2)+y^(2)+2gx+2fy+c=0 bisects the circumference of the circles x^(2)+y^(2)=6,x^(2)+y^(2)-6x-4y+10=0 and x^(2)+y^(2)+2x+2y-2=0

If the circle x^(2)+y^(2)+2gx+2fy+c=0 bisects the circumference of the circle x^(2)+y^(2)+2g'x+2f'y+c'=0 then prove that 2g'(g-g')+2f'(f-f')=c-c'