Basics of Parabola

What is the formula of eccentricity of parabola?

Given the conic ${\left(3x+4y+5\right)}^2=100\left(4x-3y-10\right)$ then distance between its focus and vertex is

What is a parabola?

Let $P$ be a point, different from $(0,0)$, on the parabola $y^2=4x$ whose focus is at $F$. Let $T$ be the foot of the perpendicular drawn from $P$ on to the directrix of the parabola. The least distance of the point $(0,0)$ from the orthocentre of triangle $PFT$ as $P$ moves on the parabola is

The axis of the parabola for the parabola $x^2=4ay$, where $a$  is a positive integer is along $x$-axis.

The axis of the parabola for the parabola $y^2=4ax$, where $a$  is a positive integer is 

For every $a\in \mathrm{ℝ}$, let $P_a$ be the parabola given by $y=x^2+2ax+a$. Then

If orthocentre of a triangle formed by $A\left(t_1\right),B\left(t_2\right),C\left(t_3\right)$ on parabola $y^2=4ax$ is the focus then $\left|t_1{t}_2+t_2{t}_3+t_3{t}_1\right|=$

Find the auxiliary circle for parabola $x^2+4x+4y+16=0$.

The vertex of a parabola is $\left(1,2\right)$ and its axis is parallel to $y-\mathrm{axis}$. If parabola passes through $\left(0,6\right)$, then the length of its latus rectum is _____

The function corresponding to the graph shown below is

The vertex of the parabola $x^2=8y-1$ is

If the point $(a, 2\mathrm{a})$ is an interior point of the region bounded by the parabola $y^2=16\mathrm{x}$ and the double ordinate through focus, then $\_\_\_$

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

If the line $2bx+3cy+4d=0$ passes through the points of intersection of $y^2=4ax$ and $x^2=4ay,$ then $\_\_\_\_\_\_\_$

If the coordinates of the ends of a focal chord of the parabola $x^2=4ay$ are $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right),$ then _______

If the Cartesian co-ordinates of the point on the parabola ${\mathrm{y}}^2=12\mathrm{x}$ whose parameter is $2$ is $\left(p,q\right) \mathrm{then} p+q=$

Value of $p$ when the parabola $y^2=4px$ passes through the point $\left(3, -2\right)$ is

The equation $y^2-8y-x+19=0$ represents

If the equation of a parabola is given as $5x^2-30x+2y=0$, then find the equation of its directrix.