Let `C_1`and `C_2` be two circles with `C_2` lying inside `C_1` A circle C lying inside `C_1` touches `C_1` internally and `C_2` externally. Identify the locus of the centre of C

Let C_1 and C_2 be two circles with C_2 lying inside C_1 . A circle C lying inside C_1 touches C_1 internally and C_2 externally. Statement : 1 Locus of centre of C is an ellipse. Statement (2) The locus of the point which moves such that the sum of its distances from two fixed points is a constant greater than the distance between the two fixed points is an ellipse. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Let C , C_1 , C_2 be circles of radii 5,3,2 respectively. C_1 and C_2 , touch each other externally and C internally. A circle C_3 touches C_1 and C_2 externally and C internally. If its radius is m/n where m and n are relatively prime positive integers, then 2n-m is:

C_1 and C_2 are fixed circles of radii r_1 and r_2 touches each other externally. Circle 'C' touches both Circles C_1 and C_2 extemelly. If r_1/r_2=3/2 then the eccentricity of the locus of centre of circles C is

A circle C_(1) of radius 2 units rolls o the outerside of the circle C_(2) : x^(2) + y^(2) + 4x = 0 touching it externally. The locus of the centre of C_(1) is

A circle is given by x^2 + (y-1) ^2 = 1 , another circle C touches it externally and also the x-axis, then the locus of center is:

Let ABC be a triangle and a circle C_1 drawn lying inside the triangle touching its incircle C_2 externally and also touching its two sides AB and AC. Show that the ratio of radii of the circles C_1 and C_2 is equal to tan^2((pi-A)/4)

A circle touches the line L and the circle C_(1) externally such that both the circles are on the same side of the line, then the locus of centre of the circle is :

Let ABCD be a square of side length 2 units. C_(2) is the fircle through the vertices A, B, C, D and C_(1) is the circle touching all the of the square ABCD. L is a lien through vertex A. A circle touches the line L and the circle C_(1) externally such that both the circles are on the same side of the line L. The locus of the centre of the circle is

The equation of a circle C_1 is x^2+y^2-4x-2y-11=0 A circle C_2 of radius 1 rolls on the outside of the circle C_1 The locus of the centre C_2 has the equation

Consider three circles C_1, C_2 and C_3 such that C_2 is the director circle of C_1, and C_3 is the director circle of C_2 . Tangents to C_1 , from any point on C_3 intersect C_2 , at P and Q . Find the angle between the tangents to C_2 at P and Q. Also identify the locus of the point of intersec- tion of tangents at P and Q .