Statement $14 x^2+y^2-4 x y-30 x-50 y+40=0$ is the equation of parabola having $(2,3)$ as its focus and $x+2 y+5=0$ as its directrix.

Statement II The equation of the directrix of the parabola $x^2-4 x+16 y+52=0$ is $y+1=0$

Which of the above statements is (are) true?

The cartesian eql tion of the parabola $x=-2+2 t^2, y=2+4 t$ is

The vertex and the focus of the parabola $2 x^2+5 y-6 x+1=0$ respectively, are

The axis of a parabola is along the line $y=x$ and the distance of its vertex $A$ from $(0,0)$ is $\sqrt{2}$ and that of its focus $S$ from $(0,0)$ is $2 \sqrt{2}$. If $A$ and $S$ lie in first quadrant, then the equation of the parabola in parametric form is