Let $A$ and $B$ be two distinct points on the parabola $y^2 = 4x$. If the axis of the parabola touches a circle of radius $r$ having $AB$ as its diameter,then the slope of the line joining $A$ and $B$ can be

The equation ${y^2} - 2x - 2y + 5 = 0$ represents:

The points of intersection of the parabolas $y^2=5x$ and $x^2=5y$ lie on the line

If the normal drawn from the point $(t_1^2, 2t_1)$ to the parabola $y^2 = 4x$ intersects the parabola again at the point $(t_2^2, 2t_2)$,then -

Let a conic $C$ pass through the point $(4,-2)$ and $P(x, y), x \geq 3$,be any point on $C$. Let the slope of the line touching the conic $C$ only at a single point $P$ be half the slope of the line joining the points $P$ and $(3,-5)$. If the focal distance of the point $(7,1)$ on $C$ is $d$,then $12d$ equals ...........

Find the coordinates of the focus,axis of the parabola,the equation of the directrix,and the length of the latus rectum for $y^{2}=10x$.