If $x-2=t^2$ and $y=2t$ are the parametric equations of the parabola $y^2=a(x-b)$,then the value of $a+b$ equals

The axis of the parabola $x^2 - 4x - 3y + 10 = 0$ is

For the parabola $y^2+6y-2x=-5$,consider the following statements:
$I$. The vertex is $(-2, -3)$.
$II$. The directrix is $y+3=0$.
Which of the following is correct?

Let the directrix of the parabola $P : y^2 = 8x$, cut $x$-axis at the point $A$. Let $B(\alpha, \beta)$, $\alpha > 1$, be a point on $P$ such that the slope of $AB$ is $3/5$. If $BC$ is a focal chord of $P$, then six times the area of $\triangle ABC$ is :

If $\theta$ is the acute angle between the tangents drawn from the point $(1,5)$ to the parabola $y^2=9x$,then:

If the parabola $x^{2}=ay$ makes an intercept of length $\sqrt{40}$ units on the line $y-2x=1$, then $a$ is equal to