Tag: hyperbola

The
eccentricity of the hyperbola whose asymptotes are $3x + 4y = 2{\text{ and }}4x - 3y + 5 = 0$  

The equation of the conjugate axis of the hyperbola $\frac{{{{\left( {y - 2} \right)}^2}}}{9} - \frac{{{{\left( {x + 3} \right)}^2}}}{{16}} = 1$ is

The eccentricity of the conjugate hyperbola of the hyperbola $x^{2} - 3y^{2} = 1$ is

If variable has its interceptson the coordinates axes $e$ and $e'$ where $e/2$ and $e'/2$ are the eccentricities of hyperbola and conjugate hyperbola, Then the line always touches the circle $x^{2}+y^{2}=r^{2}$, where $r=$ 

Let $e$ be the eccentricity of a hyperbola $\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}=1$, and $f(e)$ be the eccentricity of hyperbola $-\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1$, then $\displaystyle \int _{ 1 }^{ 3 } \underbrace { fff.....f\left( e \right)  } _{ n\quad times } de$ is equal to

$e _{1}$ and $e _{2}$ are respectively the eccentricities of a hyperbola and its conjugate then  $\dfrac{1}{e^{2} _{1}}$+$\dfrac{1}{e^{2} _{2}}$=1.

The eccentricity of the conjugate hyperbola of the hyperbola $x^{2}-3y^{2}=1$ is 

The area of quadrilateral formed by focil hyperbola $\dfrac{x^2}{4}-\dfrac{y^2}{3}=1$ & its conjugate hyperbola is

The eccentricity of the hyperbola length of whose conjugate axis is equal to half of the distance betweet the foci is 

Assertion(A): lf the lines $3x+y+p=0$ and $2x+5y-3=0$ are conjugate with respect to $3x^{2}-2y^{2}=6$ then $\mathrm{p}=1$

Reason(R): lf the lines $l _{1}x+m _{1}y+n _{1}=0$ and $l _{2}x+m _{2}y+n _{2}=0$ are conjugate with respect to the hyperbola $\mathrm{S}=0$ is $a^{2}l _{1}l _{2}+b^{2}m _{1}m _{2}=n _{1}n _{2}$