Tangent and Normal to a Parabola

The tangents drawn at P and Q on the circumference of a circle intersect at A. If$\angle \mathrm{PAQ}$ is $68°$ , then the measure of $\angle \mathrm{APQ}$ is equal to______.

If the two parabolas $y^2=4x$ and $y^2=\left(x-k\right)$ have a common normal other than $x$-axis, then value of '$k$' can be

A circle $S$ having centre $(\alpha ,\beta )$ intersect the parabola $y^2=4x$ at three points $A, B$ and $C$ such that normals at $A, B$ and $C$ are concurrent at $(9,6)$ and $O$ is origin. Then,

The locus of point of intersection of the three normals to the parabola $y^2=4ax$, two of which are inclined at right angled to each other is:

The tangents at the extremities of the latus rectum of the parabola $y^2=4ax$ meet at

The equation of the tangent at $\left(3,-6\right)$ to the parabola $y^2=12x$ is

Let $P$ denote a parabola in the plane and let a point $A\in P$ be given. How many lines $l$ in the plane satisfy $l\cap P=\left\{A\right\}?$

The slope of the normal to the parabola $y=\frac{x^2}{4}-2$ passing through the point $\left(10, -1\right)$ is

From a point $\left(C, 0\right)$ three normal are drawn to the parabola $y^2=x$ . Then

If two tangents are drawn from the point $\left(-1,-6\right)$ two tangents are drawn to the parabola $y^2=4x$. Then, the angle between two tangents is

Consider a parabola $y^2=4ax$, If the normals at points $P\left(t_1\right)$ and $Q\left(t_2\right)$ on the parabola intersect at $R$ on the curve then

If two tangents drawn from a point $P$ to the parabola $y^2=4x$ are at right angles, then the locus of $P$ is

The line $x+y=6$ is a normal to the parabola $y^2=8x$ at the point

If $y=mx+4$ is a tangent to both the parabolas, $\mathrm{}{y}^2=4x$ and $x^2=2by,$ then $b$ is equal to

If$2x+3y=\alpha , x-y=\beta$ and $kx+15y=r$ are $3$ concurrent normals of parabola $y^2=\lambda x$, then the value of $k$ is

The point on the parabola $y^2=8x$ at which the normal is inclined at ${60}^{°}$ to the $x$-axis has the coordinates

The equation of tangent with slope $\frac{2}{7}$ to Parabola $2x^2=7y$ is ......

If$2x+3y=\alpha , x-y=\beta$ and $kx+15y=r$ are $3$ concurrent normals of parabola $y^2=\lambda x$, then the value of $k$ is

The equation of the common tangent to the curves $y^2=4x$ and $x^2+32y=0$ is $x+by+c=0$. The value of $\left|{\sin }^{–1}\left(\sin 1\right)+{\sin }^{–1}\left(\sin b\right)+{\sin }^{–1}\left(\sin c\right)\right|$ is equal to

Tangents are drawn from a point $P$ to parabola $y^2=16x$ enclosing an angle of $45°$. Then, locus of point $P$ will be