Amit M Agarwal Solutions for Chapter: Parabola, Exercise 2: Work Book Exercise 14.2

A tangent to the parabola $y^2=4ax$ is inclined at $\frac{\pi }{3}$ with the axis of the parabola. The point of contact is

The equation of tangent to the parabola $y^2=9x$ which goes through the point $\left(4,10\right),$ is

Let $A, B$ and $C$ be three points taken on the parabola $y^2=4ax$ with coordinates $\left(a{t}_i^2,2a{t}_i\right)$ $i=1, 2, 3,$ where $t_1, t_2$ and $t_3$ are in $\mathrm{AP}$. If $A{A}^{\mathit{\text{'}}}\mathit{,}\mathit{ }B{B}^{\mathit{\text{'}}}$ and $C{C}^{\text{'}}$, are focal chords and coordinates of $A^{\text{'}},B^{\text{'}},C^{\text{'}}$are $\left(a{t}_i^{\text{'}2},2a{t}_i^{\text{'}}\right), i=1, 2, 3$ then $t_1^{\text{'}}, t_2^{\text{'}}$and $t_3^{\text{'}}$ are in

If a focal chord of $y^2=16x$ is a tangent to ${\left(x-6\right)}^2+y^2=2$, then the values of the slope of this chord will be

The circle $x^2+y^2-2x-6y+2=0$ intersects the parabola $y^2=8x$ orthogonally at the point $P$. The equation of the tangent to the parabola at $P$ can be

From a point $T$, a tangent is drawn at the point $P\left(16,16\right)$ of the parabola $y^2=16x$. If $S$ is the focus of the parabola, then $\angle TPS$ can be equal to

The angle between the tangents drawn from the point $\left(1,4\right)$  to the parabola $y^2=4x$ is