If a parabola touches the lines `y = x and y =-x` at `P(3,3) and Q(2,-2)` respectively, then

A variable line through the point (p, q) cuts the x and y axes at A and B respectively. The lines through A and B parallel to y-axis and x-axis respectively meet at P . If the locus of P is 3x+2y-xy=0 , then (A) p=2, q=3 (B) p=3, q=2 (C) p=2, q=-3 (D) p=-3, q=-2

A variable line through the point (p, q) cuts the x and y axes at A and B respectively. The lines through A and B parallel to y-axis and x-axis respectively meet at P . If the locus of P is 3x+2y-xy=0 , then (A) p=2, q=3 (B) p=3, q=2 (C) p=2, q=-3 (D) p=-3, q=-2

A variable chord PQ of the parabola y^(2)=4x is down parallel to the line y=x. If the parameters of the points y=x .If the parabola be p and q respectively then p+q is equal to:

The common tangent of Parabola y^2=4x and Hyperbola (x^2)/4-(y^2)/3=1 touches them at P and Q respectively, then Q can be (4, 3) (2) (3, 4) (-4,-3) (4) (4,-3)

The circle C1 : x^2 + y^2 = 3 , with center at O, intersects the parabola x^2 = 2y at the point P in the first quadrant. Let the tangent to the circle C1 at P touches other two circles C2 and C3 at R2 and R3, respectively. Suppose C2 and C3 have equal radii 2sqrt(3) and centers Q2 and Q3, respectively.If Q_2 and Q_3 lies on the y-axis, then

The circle C1 : x^2 + y^2 = 3 , with center at O, intersects the parabola x^2 = 2y at the point P in the first quadrant. Let the tangent to the circle C1 at P touches other two circles C2 and C3 at R2 and R3, respectively. Suppose C2 and C3 have equal radii 2sqrt(3) and centers Q2 and Q3, respectively.If Q_2 and Q_3 lies on the y-axis, then

A variable chord PQ of the parabola y^(2) = 4x is drawn parallel to the line y = x. If the parameters of the points P & Q on the parabola are p & q respectively, show that p + q = 2. Also show that the locus of the point of intersection of the normals at P & Q is 2x - y = 12.

A parabola (P) touches the conic x^2+xy+y^2-2x-2y+1=0 at the points when it is cut by the line x+y+1=0. The length of latusrectum of parabola (P) is

A parabola (P) touches the conic x^2+xy+y^2-2x-2y+1=0 at the points when it is cut by the line x+y+1=0. The length of latusrectum of parabola (P) is