The vertex of the parabola $3x - 2y^2 - 4y + 7 = 0$ is

If the point on the curve $y^{2}=6x$,nearest to the point $\left(3, \frac{3}{2}\right)$ is $(\alpha, \beta)$,then $2(\alpha+\beta)$ is equal to $.....$

If a point $P$ moves such that its distances from the point $A(1, 1)$ and the line $x+y+2=0$ are equal,then the locus of $P$ is

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 equation of any normal to the parabola ${y^2} = 4a(x - a)$ is

The length of the latus rectum of the parabola $y^2+8x-2y+17=0$ is