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`

Find the equation of the circle passing through (1,0)a n d(0,1) and having the smallest possible radius.

A circle has radius 3u n i t s and its centre lies on the line y=x-1. Find the equation of the circle, if it passes through (7,3)dot

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

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

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

The centre of a circle (1, 1) and its radius is 5 units. If the centre is shifted along the line y-x = 0 through a dis-tance sqrt2 units. Find the equation(s) of the circle(s) in the new position.

If A B is a focal chord of x^2-2x+y-2=0 whose focus is S and A S=l_1, then find B Sdot

If A B is a focal chord of x^2-2x+y-2=0 whose focus is S and A S=l_1, then find B Sdot

The equation of a circle S_1 is x^2 + y^2 = 1 . The orthogonal tangents to S_1 meet at another circle S_2 and the orthogonal tangents to S_2 meet at the third circle S_3 . Then (A) radius of S_2 and S_3 are in ratio 1 : sqrt(2) (B) radius of S_2 and S_1 are in ratio 1 : 2 (C) the circles S_1, S_2 and S_3 are concentric (D) none of these