Consider two straight lines, each of which is tangent to both the circle x² + y² = (1/2) and the parabola y² = 4x. Let these lines intersect at the point Q. Consider the ellipse whose centre is at the origin O(0, 0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is $$\sqrt 2 $$, then which of the following statement(s) is (are) TRUE?

If $$2x - y + 1 = 0$$ is a tangent to the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {16}} = 1$$ then which of the following CANNOT be sides of a right angled triangle?

If a chord, which is not a tangent, of the parabola y² = 16x has the equation 2x + y = p, and mid-point (h, k), then which of the following is(are) possible value(s) of p, h and k?

Let $$P$$ be the point on the parabola $${y^2} = 4x$$ which is at the shortest distance from the center $$S$$ of the circle $${x^2} + {y^2} - 4x - 16y + 64 = 0$$. Let $$Q$$ be the point on the circle dividing the line segment $$SP$$ internally. Then