Two circle `S_1 and S_2` with centre `C_1&C_2` intersect at X&Y. Secants `L_1&L_2` are drawn to `S_1&S_2` to intersect at`X_1,Y_1 and X_2,Y_2` rwspectively. If `L_1&L_2` intersect at Z in exterior ragions of `S_1 and S_2` and `ZX_1 ZY_1 = ZX_2 ZY_2`, then

If a circle S intersects circles S_1 and S_2 orthogonally. Prove that the centre of S lies on the radical axis of S_1 and S_2 .

l_1 and l_2 are the side lengths of two variable squares S_1, and S_2 , respectively. If l_1=l_2+l_2^3+6 then rate of change of the area of S_2 , with respect to rate of change of the area of S_1 when l_2 = 1 is equal to

Let a given line L_1 intersect the X and Y axes at P and Q respectively. Let another line L_2 perpendicular to L_1 cut the X and Y-axes at Rand S, respectively. Show that the locus of the point of intersection of the line PS and QR is a circle passing through the origin

Let a given line L_1 intersect the X and Y axes at P and Q respectively. Let another line L_2 perpendicular to L_1 cut the X and Y-axes at Rand S, respectively. Show that the locus of the point of intersection of the line PS and QR is a circle passing through the origin

Let a given line L_1 intersect the X and Y axes at P and Q respectively. Let another line L_2 perpendicular to L_1 cut the X and Y-axes at Rand S, respectively. Show that the locus of the point of intersection of the line PS and QR is a circle passing through the origin

Let a line L_(1):3x+2y-6=0 intersect the x and y axes at P and Q respectively.Let another line L_(2) perpendicular to L_(1) cut the x and y axes at R and S respectively.The locus of point of intersection of the lines PS and QR is

Let x^2/a^2+y^2/b^2=1 and x^2/A^2-y^2/B^2=1 be confocal (a > A and a> b) having the foci at s_1 and S_2, respectively. If P is their point of intersection, then S_1 P and S_2 P are the roots of quadratic equation

Let x^2/a^2+y^2/b^2=1 and x^2/A^2-y^2/B^2=1 be confocal (a > A and a> b) having the foci at s_1 and S_2, respectively. If P is their point of intersection, then S_1 P and S_2 P are the roots of quadratic equation

Let x^2/a^2+y^2/b^2=1 and x^2/A^2-y^2/B^2=1 be confocal (a > A and a> b) having the foci at s_1 and S_2, respectively. If P is their point of intersection, then S_1 P and S_2 P are the roots of quadratic equation