Home
Class 12
MATHS
The number of common tangents to the cir...

The number of common tangents to the circles `x^(2) + y^(2) = 4 and x^(2)+y^(2)-6x-8y=24` is

A

0

B

1

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `x^(2)+y^(2) = 4`
Centre `-=C_(1)-=(0,0)and R_(1)=2`
Again, `x^(2)+y^(2)-6x-8y-24=0 " then "C_(2)-=(3,4)`
and `R_(2)=7`
Again, `C_(1)C_(2)=5= R_(2)-R_(1)`
Therefore, the given circles touch internally such that, they can have just one common tangent at the point of contact.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the number of common tangent to the circles x^2+y^2+2x+8y-23=0 and x^2+y^2-4x-10 y+9=0

Equation of a common tangent to the circle x^(2) + y^(2) - 6x = 0 and the parabola, y^(2) = 4x , is

If y=4x+c is a tangent to the circle x^(2)+y^(2)=9 , find c.

If y=2x+c is tangent to the circle x^(2)+y^(2)=16 find c.

Find the number of common tangents that can be drawn to the circles x^2+y^2-4x-6y-3=0 and x^2+y^2+2x+2y+1=0

How the following pair of circles are situated in the plane ? Als, find the number of common tangents . (i) x^(2)+(y-1)^(2)=9 and (x-1)^(2)+y^(2)=25 (ii) x^(2)+y^(2)-12x-12y=0 and x^(2)+y^(2)+6x+6y=0

Find the equations to the common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=0

Find the locus of a point which moves so that the ratio of the lengths of the tangents to the circles x^2+y^2+4x+3=0 and x^2+y^2-6x+5=0 is 2: 3.

The sum of the slopes of the lines tangent to both the circles x^2+y^2=1 and (x-6)^2+y^2=4 is________