Embibe Experts Solutions for Chapter: Parabola, Exercise 1: WBJEE 2020

The equation of the latus rectum of a parabola is $x+y=8$ and the equation of the tangent at the vertex is $x+y=12.$ Then, the length of the latus rectum is

Consider the parabola $y^2=4x$. Let $P$ and $Q$ be points on the parabola where $P(4,-4)$ and $Q(9,6) .$ Let $R$ be a point on the arc of the parabola between $P$ and $Q .$ Then, the area of $\Delta PQR$ is largest when

Let $A,B$ be two distinct points on the parabola $y^2=4x$. If the axis of the parabola touches a circle of radius $r$ having $AB$ as diameter, the slope of the line $AB$ is

The length of the chord of the parabola $y^2=4ax(a>0)$ which passes through the vertex and makes an acute angle $\alpha$ with the axis of the parabola is

If the line $y=x$ is a tangent to the parabola $y=a{x}^2+bx+c$ at the point $\left(1,1\right)$ and the curve passes through $\left(-1,0\right)$, then

Let $P\left(a{t}^2, 2at\right),Q,R\left(a{r}^2, 2ar\right)$ be three points on a parabola $y^2=4ax$. If $PQ$ is the focal chord and $PK, QR$ are parallel where the co-ordinates of $K$ is $(2a, 0),$ then the value of $r$ is

Number of common tangents of $y=x^2$ and $y=-x^2+4x-4$ is