Let locus L of a variable point `P(x, y) is x^3 +y^3 = 1 - 3xy, x != - 1`. A circle with center `C_1(2, 2)` and radius r touches L at Q(a, b) and line `x+y=c, (c != 1) at R(d, e)`, then

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a)x+3y=2 (b) x+2y=2( c) x+y=2 (d) none of these

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=3 (c) x+y=2 (d) none of these

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=2 (c) x+y=2 (d) none of these

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=2 (c) x+y=2 (d) none of these

Let the line L : sqrt(2)x y =alpha pass through the point of the intersection P (in the first quadrant) of the circle x^2 y^2 = 3 and the parabola x^2 = 2y . Let the line L touch two circles C_1 and C_2 of equal radius 2 sqrt 3 . If the centres Q_1 and Q_2 of the circles C_1 and C_2 lie on the y-axis, then the square of the area of the triangle PQ_1Q_2 is equal to ___________.

A straight line L passing through the point P(-2,-3) cuts the lines, x + 3y = 9 and x+y+1=0 at Q and R respectively. If (PQ) (PR) = 20 then the slope line L can be (A) 4 (B) 1 (C) 2 (D) 3

Consider the lines L_1 and L_2 defined by L_1:xsqrt2+y-1=0 and L_2:xsqrt2-y+1=0 For a fixed constant lambda , let C be the locus of a point P such that the product of the distance of P from L_1 and the distance of P from L_2 is lambda^2 . The line y=2x+1 meets C at two points R and S, where the distance between R and S is sqrt(270) . Let the perpendicular bisector of RS meet C at two distinct points R' and S' . Let D be the square of the distance between R' and S'. The value of D is

Consider the lines L_1 and L_2 defined by L_1:xsqrt2+y-1=0 and L_2:xsqrt2-y+1=0 For a fixed constant lambda , let C be the locus of a point P such that the product of the distance of P from L_1 and the distance of P from L_2 is lambda^2 . The line y=2x+1 meets C at two points R and S, where the distance between R and S is sqrt(270) . Let the perpendicular bisector of RS meet C at two distinct points R' and S' . Let D be the square of the distance between R' and S'. The value of lambda^2 is

The locus of the centre of the circle touching the line 2x-y=1 at (1, 1) and also touching the line x+2y =1 is : (A) x+3y = 2 (B) x+2y=3 (C) x+y=2 (D) none of these