If two tangents drawn from a point $P$ to the parabola $y^2 = 4x$ are at right angles,then the locus of $P$ is:

The length of the latus rectum of the parabola $(x-2)^2+(y-3)^2=\frac{1}{25}(3x-4y+7)^2$ is

If the focus of a parabola is $(1, 0)$ and its directrix is $x + y = 5$,what is its vertex?

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:

The area of the triangle formed by the lines joining the vertex of the parabola $x^2 = 12y$ to the ends of its latus rectum is .................. $sq. \ unit$.

The equation of the latus rectum of the parabola $x^2 + 4x + 2y = 0$ is: