Prove that the lines joining the ends of latus rectum of the parabola `y^(2) = 4ax` with the point of intersection of its axis and directrix are at right angles.

Find the latus rectum of the parabola (y-3)^2=6(x-2)

The length of latus rectum of the parabola 3x^(2) =- 8y is _

If a + bne 0 , find the coordinates of focus and the length of latus rectum of the parabola y^(2) = 2 mx which passes through the point of intersection of the straight lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 .

Find the area of the parabola y^(2) = 4ax bounded by its latus rectum.

The coordinates of one of the end-points of the latus rectum of the parabola (y - 1)^(2) = 2(x + 2 ) are _

Find the equations of normal to the parabola y^2=4a x at the ends of the latus rectum.

A double ordinate of the parabola y^(2) = 4 ax is of length 8a . Prove that the lines joining the vertex to its two ends are at right angles .

The point of intersection of the tangents to the parabola y^(2)=4ax at the points t_(1) and t_(2) is -

If the length of the double ordinate of a parabola y^2=4ax is 8a.Prove that the line joining the vertex to its two ends are at right angle.

The coordinates of the two ends of latus rectum of a parabola are (8,1) and (-4,1) , find the equation of the parabola.