Home
Class 12
MATHS
If the circle x^2+y^2=1 is completely co...

If the circle `x^2+y^2=1` is completely contained in the circle `x^2+y^2+4x+3y+k=0` , then find the values of `kdot`

Text Solution

Verified by Experts

Given circles are
`x^(2)+y^(2)=1` (1)
and `x^(2)+y^(2)+4x+3y+k=0` (2)
`C_(1)(0,0),r_(1)=1`
`C_(2)(-2,-3//2),r_(2)=sqrt(4+(9)/(4)-k)=sqrt((25)/(4)-k)`.
Circle (1) is completely contained by circle (2).
`implies C_(1)C_(2) lt r_(2) -r_(1)`
`implies sqrt(4+(9)/(4))ltsqrt((25)/(4)-k)`
`implies (5)/(2)+1ltsqrt((25)/(4)-k)`
`implies (25)/(4)-k gt(49)/(4)`
`implies k lt - 6`
Also , for these values of `k, (25)/(4)-k gt 0`.
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

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

If the tangents are drawn to the circle x^2+y^2=12 at the point where it meets the circle x^2+y^2-5x+3y-2=0, then find the point of intersection of these tangents.

If the length tangent drawn from the point (5, 3) to the circle x^2+y^2+2x+k y+17=0 is 7, then find the value of kdot

The circle x^2 + y^2 - 4x + 6y + c = 0 touches x axis if

If y = 2sqrt2x+c is a tangent to the circle x^(2) +y^(2) = 16 , find the value of c.

Let P be any moving point on the circle x^2+y^2-2x=1. A B be the chord of contact of this point w.r.t. the circle x^2+y^2-2x=0 . The locus of the circumcenter of triangle C A B(C being the center of the circle) is 2x^2+2y^2-4x+1=0 x^2+y^2-4x+2=0 x^2+y^2-4x+1=0 2x^2+2y^2-4x+3=0

Let P be any moving point on the circle x^2+y^2-2x=1. A B be the chord of contact of this point w.r.t. the circle x^2+y^2-2x=0 . The locus of the circumcenter of triangle C A B(C being the center of the circle) is 2x^2+2y^2-4x+1=0 x^2+y^2-4x+2=0 x^2+y^2-4x+1=0 2x^2+2y^2-4x+3=0

If the circle x^2+y^2-4x-8y-5=0 intersects the line 3x-4y=m at two distinct points, then find the values of mdot