Conic Section

The asymptotes of a hyperbola passes through the

The number of tangents to the hyperbola $\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}=1$ that can be drawn from an external point is

Director circle of $\dfrac{x^{2}}{16}+\dfrac{y^{2}}{9}=1$ is

The distance of the focus of the parabola $y^{2}=16 x$ from its directrix is…

The equation of the tangent at a point $P(t)$ where ' $t$ ' is any parameter to the parabola $y^{2}=4ax$, is

The equation of the director circle of the hyperbola $\dfrac{x^{2}}{16}-\dfrac{y^{2}}{4}=1$ is given by

The eccentricity of the conic $16x^{2}+25y^{2}=400$ is

What is the eccentricity of hyperbola whose vertices and foci are ($\pm$2, 0) and ($\pm$3, 0) respectively?

A parabola has the origin as its focus and the line $x=2$ as the directrix. Then the vertex of the parabola is at

The distance between the directrices of the hyperbola $x^{2}-y^{2}=9$ is

The equation of the ellipse whose latus rectum is 8 and whose eccentricity is $\dfrac{1}{\sqrt{2}}$, referred to the principal axes of coordinates, is

The length of the latus rectum of the parabola $9x^{2}$ – 6x + 36y + 19 = 0

The line $y=\mathrm{m} x+3$ is tangent to the parabola $y^{2}=4 x$, if the value of m is

The line $y=2x+c$ is a tangent to the parabola $y^{2}=16x$, if $c$ equals

Find the foci of the hyperbola with vertices at $(0,\pm 6)$ and $e=\dfrac{5}{3}$.