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

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

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 point on the parabola $y^2=4ax$ nearest to focus has its abscissa

The shortest distance between the line $x-y=1$ and the curve $x^2=2y$ is:

Let $P, Q$ be the points with parameters $t_1, t_2$ on the parabola $y^2=4ax.$ If the normals at $P, Q$ meet on the parabola at $R\left(t_3\right),$ then

The equation of common normal to the circle $x^2+y^2-12x+16=0$ and parabola $y^2=4x$ is

Normals at $A,B,C$ are drawn to $y^2=4x$ which intersects at $P\left(3,0\right)$. Then the equation of circumcircle of $\Delta ABC$ is