The axis of the parabola $x^{2}+2 x y+y^{2}-5 x+5 y-5=0$ is

The shortest distance between the line $y - x = 1$ and the curve $x = y^2$ is

The area of the triangle formed by the lines joining the vertex of the parabola $x^{2}=12y$ to the extremities of its latus rectum is

The point of contact of the tangent to the parabola $y^2=9x$ which passes through the point $(4, 10)$ and makes an angle $\theta$ with the positive side of the axis of the parabola where $\tan \theta > 2$,is

The parabola $x^2=4ay$ makes an intercept of length $\sqrt{40}$ units on the line $y=2x+1$. Find the value of $4a$.

If the line $y = 4 + kx$,$k > 0$,is the tangent to the parabola $y = x - x^{2}$ at the point $P$ and $V$ is the vertex of the parabola,then the slope of the line through $P$ and $V$ is