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

If the parabola y^(2)=4ax,a>0 cuts the hyperbola xy=sqrt(2) at right angles,then a=

If the segment intercepted by the parabola y^2=4a x with the line l x+m y+n=0 subtends a right angle at the vertex, then

If a normal of slope m to the parabola y^2 = 4 a x touches the hyperbola x^2 - y^2 = a^2 , 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=4a x passing through the point (4a ,0) subtends a right angle at the vertex of the parabola.

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

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.

The curve x = y^(2) and xy = k cut at right angles if

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

If the ellipse x^2/a^2+y^2/b^2=1 (b > a) and the parabola y^2 = 4ax cut at right angles, then eccentricity of the ellipse is