The equation of the parabola whose focus is $(6,0)$ and directrix is $x=-6$ is

The angle between tangents to the parabola $y^2 = 4ax$ at the points where it intersects with the line $x - y - a = 0$ is

If the parabola $y = \alpha x^{2} - 6x + \beta$ passes through the point $(0, 2)$ and has its tangent at $x = \frac{3}{2}$ parallel to the $X$-axis,then:

The locus of the feet of the perpendiculars drawn from the vertex of the parabola $y^2 = 4ax$ upon all such chords of the parabola which subtend a right angle at the vertex is

The points of intersection of the parabolas $y^2=5x$ and $x^2=5y$ lie on the line

The points $(at_1^2, 2at_1)$,$(at_2^2, 2at_2)$,and $(a, 0)$ will be collinear,if