Dr. SK Goyal Solutions for Chapter: Parabola, Exercise 8: FILL IN THE BLANKS

The length of the Latus rectum of the parabola $x=a{y}^2+by+c$ is _____

If the normal at $P\left(t\right)$  on $y^2=4ax$ meets the curve again at $Q$, the point $R$ on the curve, the normal at which also passes through $Q$ has co-ordinates $\left(\_\_\right)$

The diameter of the parabola $y^2=6x$ corresponding to the system of parallel chords $3x-y+c=0$ is ______.

A focal chord of $y^2=4ax$ meets in $P$ and $Q$. If $S$ is the focus, then
$\frac{1}{SP}+\frac{1}{SQ}=$_____.

Let $C_1$ and $C_2$ be respectively, the parabolas $x^2=y-1$ and $y^2=x-1$. Let $P$ be any point on $C_1$ and $Q$ be any point on $C_2$. Let $P_1$ and $Q_1$ be the reflections of $P$ and $Q$ respectively with respect to the line $y=x$ then $P_1$ lies on and $Q_1$ lies on ______

A ray of light moving parallel to the $x$-axis gets reflected from a parabolic mirror whose equation is ${\left(y+3\right)}^2=4\left(x+1\right)$. After reflection, the ray must pass through the point ______

The focus of the parabola $x^2+y^2+2xy-2x-1=0$ is _______.

The condition that the parabola $y^2=4c(x-d)$ and $y^2=4ax$ have a common normal other than $x$-axis $\left(a>0, c>0\right),$ if $d+2c>$ _____