Home
Class 12
MATHS
The common tangent to the circles x^(2)...

The common tangent to the circles `x^(2)+y^(2) = 4 and x^(2) + y^(2) + 6x + 8y - 24 = 0` also passes through the point

A

(4, -2)

B

(-4, 6)

C

(-6, 4)

D

(6, -2)

Text Solution

Verified by Experts

The correct Answer is:
D
`x^(2) + y^(2) = 4`
`x^(2) + y^2) + 6x + 8y - 24 = 0`
`(X + 3)^(2) + (y + 4)^(2 = 49`
Clearly circle (i) & circle (ii) touches internally because `c_(1)c_(2) = |r_(1) - r_(2)|`
Equation of common tangent `s_(1) - s_(2) = 0`
`s_(1) - s_(2) = 6x + 8y - 20 = 0`
`3x + 4y = 10`
Point (6, -2 passes through the tangent
Promotional Banner

Similar Questions

Explore conceptually related problems

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

The point lying on common tangent to the circles x^(2)+y^(2)=4 and x^(2)+y^(2)+6x+8y-24=0 is

A circle passing through the intersection of the circles x ^(2) + y^(2) + 5x + 4=0 and x ^(2) + y ^(2) + 5y -4 =0 also passes through the origin. The centre of the circle is

The number of common tangents to the circles x^(2)+y^(2)-y=0and x^(2)+y^(2)+y=0 is

The common tangents to the circles x^(2) +y^(2) +2x = 0 and x^(2) +y^(2) -6x= 0 from a triangle which is :

The lengths of the common tangents of the circles x^(2)+y^(2)+4x=0 and x^(2)+y^(2)-6x=0 is

Statement 1 : The number of common tangents to the circles x^(2) + y^(2) =4 and x^(2) + y^(2) -6x - 6y = 24 is 3. Statement 2 : If two circles touch each other externally thenit has two direct common tangents and one indirect common tangent.

The point of tangency of the circles x^(2)+y^(2)-2x-4y=0 and x^(2)+y^(2)-8y-4=0 is