Tangent 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______.

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 $l\cap P=\left\{A\right\}?$

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

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

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

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

The area of the triangle formed by tangents of the parabola $y^2=8x$ at the three points on the parabola having parameter $t_1, t_2$ and $t_3$ is

The equation of tangent to the parabola $y^2=8x$ inclined at $30°$ to the $x$-axis is

The line $x+y+2=0$ is a tangent at point $A$, intersect the directrix at $B$ and tangent at vertex at $C$ respectively. If the focus of parabola is $S\left(2,0\right),$ then value of $AC·BC$ is

Let $a, b\in R$ and $a>0.$ If the tangent at the point $(2,2)$ to the circle $x^2+y^2=8$ touches the parabola, $y^2=4a\left(x-b\right),$ then $b-a$ is equal to_______.

The radius of the circle, touching the parabola ${\mathrm{y}}^2=8\mathrm{x}$ at $\left(\mathrm{2,4}\right)$ and passing through $\left(\mathrm{0,4}\right),$ is

The equation of the tangent to the parabola $y^2=16x$ having slope $4$, is

Two tangents are drawn from the exterior point $P\left(-\mathrm{1,2}\right)$ to the parabola $y^2-4x=0$ touching it at points $A \& B$, then area of $∆ABC$ (in sq. units) is equal to

If $\alpha$ is the angle between the two tangents drawn from a point $\left(–4,3\right)$ to the parabola $y^2=16x$. then the value of $\cos \alpha$ is

Tangents are drawn at the points $\mathrm{A}\left({\mathrm{t}}_1\right), \mathrm{B}\left({\mathrm{t}}_2\right) \& \mathrm{C}\left({\mathrm{t}}_3\right)$ on the parabola $y^2=4ax; (a>0)$ and these tangents meet each other to form a triangle ${\mathrm{A}}^{\text{'}}{\mathrm{B}}^{\text{'}}{\mathrm{C}}^{\text{'}}$ as shown in the given figure.

If area of $∆\mathrm{ABC}=12 sq. units$ and perimeter of $\Delta {\mathrm{A}}^{\text{'}}{\mathrm{B}}^{\text{'}}{\mathrm{C}}^{\text{'}}=6 \mathrm{units}$, then find inradius of the triangle ${\mathrm{A}}^{\text{'}}{\mathrm{B}}^{\text{'}}{\mathrm{C}}^{\text{'}}$.

The equation of the given parabola to which the line$L: m^2\left(y –10\right)–mx –1=0$ is a tangent for any real value of $m$, is 

Find the radius of circle touching the parabola $y^2=4x$ at an end of latus rectum and passing through focus of the parabola.

Equation of the common tangent to the equal parabolas$y^2=4ax \& x^2=4ay$ is

Find the locus of the Orthocentre of the triangle formed by three tangents of the parabola $(4x - 3{)}^2 =- 64(2y + 1).$