The line y = m(x + a)+a/m touch the parabola y²= 4a(x+ a) form

If the line x + y + 2 = 0 touches the parabola y² = kx, then k =

The point of contact of  2x – y + 2 = 0 to the parabolay² = 16x is

If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x₁,y₁) and (x₂,y₂) respectively, then

the equation of the parabola whose vertex is at (0,0) and focus is the point of intersection of x+y  =2, 2x –y = 4 is

The locus of the point of intersection of the perpendicular tangents to the parabola x² = 4ay is

The length of the latus rectum of the parabola 4y² + 12x – 20y + 67 = 0 is

The equation of the common tangent to y²= 8x and x²+y² – 12x + 4 = 0

The coordinate of the point on the parabola y² = 2x whose focal distance is 5/2 are

The equation of the latus rectum  of the parbola x² – 12x – 8y + 52 = 0 is