If the curve `x^2 + 2y^2 = 2` intersects the line `x + y = 1` at two points P and Q, then the angle subtended by the line segment PQ at the origin is :

If any tangent to the parabola x^(2) = 4y intersects the hyperbola xy = 2 at two points P and Q, then the mid point of line segment PQ lies on a parabola with axis along:

If any tangent to the parabola x^(2)=4y intersects the hyperbola xy=2 at two points P and Q , then the mid point of the line segment PQ lies on a parabola with axs along

The line x=2y intersects the ellipse (x^(2))/4+y^(2)=1 at the points P and Q . The equation of the circle with PQ as diameter is

The straight lines y=+-x intersect the parabola y^(2)=8x in points P and Q, then length of PQ is

A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C_1 : x^2 + y^2 + 2y -5 = 0 at two points P and Q such that PQ is a diameter of C^1 . Then the diameter of C is :

Let P be a point on the parabola y^(2) - 2y - 4x+5=0 , such that the tangent on the parabola at P intersects the directrix at point Q. Let R be the point that divides the line segment PQ externally in the ratio 1/2 : 1. Find the locus of R.

A straight line through the origin 'O' meets the parallel lines 4x+2y=9 and 2x+y=-6 at points P and Q respectively.Then the point 'divides the segment PQ in the ratio