The parabola $y=4-x^2$ has vertex P. It intersects $x$-axis at A and B. If the parabola is translated from its initial position to a new position by moving its vertex along the line $y=x+4$, so that it intersects $x$-axis at B and C , then the abscissa of C will be

Let A, B the two distinct points on the parabola y² = 4x. If the axis of the parabola touches a circle of radius r having AB as diameter, the slope of the line AB is

The area of the region lying above X-axis, and included between the circle x² + y² = 2ax and the parabola y² = ax, a > 0 is

If the tangent to $${y^2} = 4ax$$ at the point $$(a{t^2},2at)$$ where | t | > 1 is a normal to $${x^2} - {y^2} = {a^2}$$ at the point $$(a\sec \theta ,a\tan \theta )$$, then