The coordinates of a moving point $P$ are $(2t^2+4, 4t+6)$. Then its locus will be a

The locus of the vertices of the family of parabolas $6y = 2a^3x^2 + 3a^2x - 12a$ is

The coordinates of the focus of the parabola described parametrically by $x=5t^2+2, y=10t+4$ (where $t$ is a parameter) are

Let $L_1, L_2$ be the lines passing through the point $P(0,1)$ and touching the parabola $9x^2+12x+18y-14=0$. Let $Q$ and $R$ be the points on the lines $L_1$ and $L_2$ such that the $\triangle PQR$ is an isosceles triangle with base $QR$. If the slopes of the lines $QR$ are $m_1$ and $m_2$,then $16(m_1^2+m_2^2)$ is equal to ..............

The radius of the smallest circle which touches the parabolas $y = x^2 + 2$ and $x = y^2 + 2$ is

What is the length of the latus rectum of the parabola $x^2 - 4x - 8y + 12 = 0$?