Embibe Experts Solutions for Chapter: Parabola, Exercise 1: Level 1

The second degree equation $x^2+4y^2-2x-4y+2=0$ represents

The coordinates of the focus of the parabola described parametrically by $x=5t^2+2,y=$$10t+4$ (where $t$ is a parameter) are

The length of the latus rectum of the parabola whose focus is $\left(\frac{u^2}{2g}\sin 2\alpha ,-\frac{u^2}{2g}\cos 2\alpha \right)$ and directrix is $y=\frac{u^2}{2g}$ is

If $P$ be a point on the parabola $y^2=3\left(2x-3\right)$ and $M$ is the foot of perpendicular drawn from $P$ on the directrix of the parabola, then the length of each side of an equilateral triangle $SMP,$ where $S$ is the focus of the parabola is

Let $y^2=16x$ be a given parabola and $L$ be an extremity of its latus rectum in the first quadrant. If a chord is drawn through $L$ with slope $-1$, then the length of this chord is

A line bisecting the ordinate $PN$ of a point $P\left(a{t}^2,2at\right), t>0$ on the parabola $y^2=4ax$ is drawn parallel to the axis to meet the curve at $Q$. If $NQ$ meets the tangent at the vertex at the point $T$, then the coordinates of $T$ are

The locus of the mid-point of the line segment joining the focus of the parabola $y^2=4ax$ to a moving point of the parabola, is another parabola whose directrix is:

 Locus of the intersection of the tangents at the ends of the normal chords of the parabola  $y^2=4ax$  is -