If the parabola `y^2=4a x ,\ a >0` cuts the hyperbola `x y=\ sqrt(2)"\ "` at right angles, then `a\ =`

The parabola y^(2)=4x cuts orthogonally the rectangular hyperbola xy=c^(2) then c^(2)=

At the point of intersection of the rectangular hyperbola xy=c^(2) and the parabola y^(2)=4ax tangents to the rectangular hyperbola and the parabola make angles theta and phi, respectively with x-axis,then

Statement 1: Normal chord drawn at the point (8,8) of the parabola y^(2)=8x subtends a right angle at the vertex of the parabola.Statement 2: Every chord of the parabola y^(2)=4ax passing through the point (4a,0) subtends a right angle at the vertex of the parabola.

If a normal of slope m to the parabola y^(2)=4ax touches the hyperbola x^(2)-y^(2)=a^(2), then

The radius of the circle whose centre is (-4,0) and which cuts the parabola y^(2)=8x at A and B such that the common chord AB subtends a right angle at the vertex of the parabola is equal to

If the planes 2x+y-2z=0and x+2y+kz=0 are at right angles, then the value of k is