S L Loney Solutions for Chapter: Conic Sections. The Parabola, Exercise 1: EXAMPLES XXV

The equation of the parabola with focus $\left(3,-4\right)$ and directrix $6x-7y+5=0$ is ${\left(ax+by\right)}^2-570x+750y+2100=0$. Find $ab$.

The equation to the parabola with focus $\left(a, b\right)$ and directrix $\frac{x}{a}+\frac{y}{b}=1$ is ${\left(ax-by\right)}^2-p{a}^{3}x-q{b}^{3}y+a^4+a^2{b}^2+b^4=0$. Find $p-q$.

The vertex, equation of axis, length of latus rectum and focus of the parabola $y^2=4x+4y$ are $(p,q)$, $y=r$, $s$ and $(0,t)$, respectively. Find $p+q+r+s+t$.

Find the vertex, equation of the axis, length of the latus rectum and focus of the parabola: $x^2+2y=8x-7$.  $(p,q)$, $x=r$, $s$ and $(t,u)$, respectively. Find $p+2q+r+2s+t+2u$.$$

If the equation of the parabola is $y^2=4y-4x$ and the coordinates of the focus of the parabola are $\left(a,b\right)$. Find $a+b$.

If the parabola $y^2=4px$ passes through the point $\left(3, -2\right)$, then the value of $9p$ is

Find the value of $p$ when the parabola $y^2=4px$ passes through the point $\left(9,-12\right)$.

Prove that the locus of a point, which moves so that its distance from a fixed line not passing through center of circle is equal to the length of the tangent drawn from it to a given circle, is a parabola. Find the position of the focus and directrix.