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`

Let T be the line passing through the points P(-2,\ 7) and Q(2,\ -5) . Let F_1 be the set of all pairs of circles (S_1,\ S_2) such that T is tangent to S_1 at P and tangent to S_2 at Q , and also such that S_1 and S_2 touch each other at a point, say, M . Let E_1 be the set representing the locus of M as the pair (S_1,\ S_2) varies in F_1 . Let the set of all straight lines segments joining a pair of distinct points of E_1 and passing through the point R(1,\ 1) be F_2 . Let E_2 be the set of the mid-points of the line segments in the set F_2 . Then, which of the following statement(s) is (are) TRUE? The point (-2,\ 7) lies in E_1 (b) The point (4/5,7/5) does NOT lie in E_2 (c) The point (1/2,\ 1) lies in E_2 (d) The point (0,3/2) does NOT lie in E_1

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

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

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

A curve C passes through (2,0) and the slope at (x , y) as ((x+1)^2+(y-3))/(x+1)dot Find the equation of the curve.

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

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 centre of a circle passing through (0,0), (1,0) and touching the CircIe x^2+y^2=9 is a. (1/2,sqrt2) b. (1/2,3/sqrt2) c. (3/2,1/sqrt2) d. (1/2,-1/sqrt2)

Find the equation of the plane passing through A(2,2,-1),B(3,4, 2)a n dC(7,0,6)dot Also find a unit vector perpendicular to this plane.

Find the equation of the plane passing through the points (1,0,-1)a n d(3,2,2) and parallel to the line x-1=(1-y)/2=(z-2)/3dot