From the point $(-1, -60)$ two tangents are drawn to the parabola $y^2 = 4x$. Then the angle between the two tangents is .................. $^o$

The centroid of the triangle formed by joining the feet of the normals drawn from any point to the parabola $y^2 = 4ax$ lies on

Which of the following lines is a normal to the parabola $y^2 = 16x$?

The equation of the parabola with vertex at $(0,0)$ and length of latus rectum equal to $\frac{16}{3}$ is:

Let $A, B$ and $C$ be the vertices of a variable right-angled triangle inscribed in the parabola $y^2 = 16x$. Let the vertex containing the right angle be $C = (4, 8)$ and the locus of the centroid of $\triangle ABC$ be a conic $C_o$. Then three times the length of the latus rectum of $C_o$ is . . . . . .

If the equation of the parabola with vertex $V \left(\frac{3}{2}, 3\right)$ and the directrix $x + 2y = 0$ is $\alpha x^2 + \beta y^2 - \gamma xy - 30x - 60y + 225 = 0$,then $\alpha + \beta + \gamma$ is equal to: