Let `L` be a normal to the parabola `y^2=4xdot` If `L` passes through the point (9, 6), then `L` is given by `

The parabola y^(2)=4ax passes through the point (2,-6), the the length of its latus rectum is . . . .

If normals drawn at three different point on the parabola y^(2)=4ax pass through the point (h,k), then show that h hgt2a .

Find the equation of the normal to the curve x^(2) = 4y which passes through the point (1, 2).

IF three distinct normals to the parabola y^(2)-2y=4x-9 meet at point (h,k), then prove that hgt4 .

Three normals to y^2=4x pass through the point (15, 12). Show that one of the normals is given by y=x-3 and find the equation of the other.

If the angle between the normal to the parabola y^(2)=4ax at point P and the focal chord passing through P is 60^(@) , then find the slope of the tangent at point P.

Find the locus of the midpoint of chords of the parabola y^2=4a x that pass through the point (3a ,a)dot

Prove that the chord y-xsqrt(2)+4asqrt(2)=0 is a normal chord of the parabola y^2=4a x . Also find the point on the parabola when the given chord is normal to the parabola.

L O L ' and M O M ' are two chords of parabola y^2=4a x with vertex A passing through a point O on its axis. Prove that the radical axis of the circles described on L L ' and M M ' as diameters passes though the vertex of the parabola.

If L is the length of the latus rectum of the hyperbola for which x=3a n dy=2 are the equations of asymptotes and which passes through the point (4, 6), then the value of L/(sqrt(2)) is_____