Let `S_1` be a circle passing through `A(0,1)` and `B(-2,2)` and `S_2` be a circle of radius `sqrt(10)` units such that `A B` is the common chord of `S_1a n dS_2dot` Find the equation of `S_2dot`

The centre of a circle passing through the points (0,0),(1,0)and touching the circle x^2+y^2=9 is

A circle passes through the points (3, 4), (-1, 2) and its radius is 5 unit, find the equation of the circle.

The ordinate of the centre of the circle passing through (0,0) and (1,0) and touching the circle x ^(2) + y^(2) =9 is-

C_1 and C_2 are circle of unit radius with centers at (0, 0) and (1, 0), respectively, C_3 is a circle of unit radius. It passes through the centers of the circles C_1a n dC_2 and has its center above the x-axis. Find the equation of the common tangent to C_1a n dC_3 which does not pass through C_2dot

Two circles C_1 and C_2 intersect in such a way that their common chord is of maximum length. The center of C_1 is (1, 2) and its radius is 3 units. The radius of C_2 is 5 units. If the slope of the common chord is 3/4, then find the center of C_2dot

Find the equation of the plane passing through A(2,2,-1),B(3,4, 2)a n dC(7,0,6)dot

S is a circle having the center at (0,a) and radius b(b < a)dot A variable circle centered at (alpha,0) and touching the circle S meets the X-axis at Ma n dN . Find the a point P on the Y-axis, such that /_M P N is a constant for any choice of alpha

Find the equation of each of the circles passing through the points : (0, 0), (1, 2), (2, 0)

Let A B C be a triangle right-angled at Aa n dS be its circumcircle. Let S_1 be the circle touching the lines A B and A C and the circle S internally. Further, let S_2 be the circle touching the lines A B and A C produced and the circle S externally. If r_1 and r_2 are the radii of the circles S_1 and S_2 , respectively, show that r_1r_2=4 area ( A B C)dot

A circle S passes through the point (0, 1) and is orthogonal to the circles (x - 1)^2 +y^2=16 and x^2+y^2=1 . Then