Tag: mathematics and statistics
Questions Related to mathematics and statistics
The equation $\dfrac{x^{2}}{29 -p} + \dfrac{y^{2}}{4 -p} =1(p\neq4, 29)$ represents -
Which of the following equations in parametric form can represent a hyperbolic profile, where $t$ is a parameter.
The transverse axis of a hyperbola is of length $2a$ and a vertex divides the segment of the axis between the centre and the corresponding focus in the ratio $2:1$. The equation of the hyperbola is
The equation of the hyperbola whose directrix is $2x + y = 1$,corresponding focus is $(1, 1)$ and eccentricity $\sqrt { 3 }$, is given by
The equation of the hyperbola whose foci are $(8,3)$ and $(0,3)$ and eccentricity$=\cfrac { 4 }{ 3 } $ is
The equation of the hyperbola whose directrix is $x + 2y = 1$, focus is $(2, 1)$ and eccentricity $2$ is
If ${ e } _{ 1 }$ is the eccentricity of the ellipse $\cfrac { { x }^{ 2 } }{ 16 } +\cfrac { { y }^{ 2 } }{ 25 } =1$ and ${ e } _{ 2 }$ is the eccentricity of the hyperbola passing through the foci of the ellipse and ${ e } _{ 1 }.{ e } _{ 2 }=1$, then the equation of the hyperbola, is :
Equation of the hyperbola whose vertices are at ($\pm3, 0$) and focii at ($\pm5, 0$) is
The equation of the conic with focus at $(1, -1)$, directrix along $x - y + 1= 0$ and with eccentricity $\sqrt{2}$ is
The tangent of a point $P$ on the hyperbola $\dfrac {x^{2}}{a^{2}}-\dfrac {y^{2}}{b^{2}}=1$ passes through the point $(0,\ -b)$ and the normal at $P$ pases through the point $(2a\sqrt {2},\ 0)$. Then the eccentricity of the hyperbola is