Home
Class 12
MATHS
lf a circle C passing through (4,0) touc...

lf a circle `C` passing through `(4,0)` touches the circle `x^2 + y^2 + 4x-6y-12 = 0` externally at a point `(1, -1),` then the radius of the circle `C` is :-

A

`sqrt(57)`

B

`2sqrt5`

C

5

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
`S=x^(2)+y^(2)+4x-6y-12`
Tangent at (1, -1)
`x-y+2(x+1)-3(y-1)=12`
`3x-4y=7`
Family of such circles , `S+lamdaL=0`
`x^(2)+y^(2)+4x-6y-12+lamda(3x-4y-7)=0`
`16+16-12+lamda(12-7)=0`
`lamda=(-20)/5=-4`
Equation of circle : `x^(2)+y^(2)-8x+10y+16=0`
Radius = 5
Promotional Banner

Similar Questions

Explore conceptually related problems

If a circle C passing through (4,0) touches the circle x^(2)+y^(2)+4x-6y-12=0 externally at a point (1,-1), then the radius of the circle C is :

If circle C passing through the point (2, 2) touches the circle x^2 + y^2 + 4x - 6y = 0 externally at the point (1, 1), then the radius of C is:

If a circle C passing through the point (4,0) touches the circle x^(2)+y^(2)+4x-6y=12 externally at the point (1,-1) ,then the radius of C is

If a circle passes through (0,0),(4,0) and touches the circle x^(2)+y^(2)=36 then the centre of circle

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

Centre of a circle passing through point (0,1) and touching the curve y=x^2 at (2,4) is

The equation of the cirele which passes through the point (1,1) and touches the circle x^(2)+y^(2)+4x-6y-3=0 at the point (2,3) on it is

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

A circle passes through (0,0) and (1,0) and touches the circle x^(2)+y^(2)=9 then the centre of circle is -

The equation of the normal at (1,2) to the circle x^(2)-y^(2)-4x-6y-12=0 is