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

The eccentricity of the  parabola y² – 2x – 6y + 5 = 0 is

The ordinate of  the centroid of the triangle formed by conormal points on the parabola y²=4ax is

If z² = (x^1/2 + y^1/2)/(x^1/3 + y^1/3), then x(∂z/∂x) + y(∂z/∂y) is :

AB,AC are tangents to a parabola y²= 4ax. If l₁,l₂,l₃ are the lengths of perpendiculars from A,B,C on any tangent to the parabola,then