The equation ` y^(2) + 4x + 4y + k = 0 ` represents a parabola whose latus rectum is _

y^2+2y-x+5=0 represents a parabola. Find equation of latus rectum.

Show that the differntial equation that represents all parabolas each of which has a latus rectum 4a and whose axes are parallel to x axis is 2ay_2+y_1^3=0 .

P (x_(1),y_(1)) and Q(x_(2),y_(2)) are two ends of a latus rectum of the ellipse x^(2) + 4y^(2) = 4 , where y_(1),y_(2) lt 0 . The equation of parabola with latus rectum PQ is _

If the parabola y^(2) =4ax passes through the centre of the circle x^(2) +y^(2) + 4x - 12 y - 4 = 0 what is the length of the latus rectum of the parabola ?

The equation of the tangent to the parabola y^(2)=4x at the end of the latus rectum in the fourth quadrant is

The equation of the tangent to the parabola y^(2)=4x at the end of the latus rectum in the fourth quadrant is