Tag: standard equation of hyperbola

General solution of the equation $ y=x\dfrac{dy}{dx}+\dfrac {dx}{dy}$ represents _____________.

Eccentricity of hyperbola$ \dfrac { { x }^{ 2 } }{ k } -\dfrac { { y }^{ 2 } }{ k } =1$

A hyperbola passes through the focus of the ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{16}=1,$ and its transverses and conjugate axes coincide with the major and minor axes of the ellipse. If the product of the eccentricites of the two curve is $1$, then the focus of the hyperbola is

The foci of the hyperbola $xy=4$ are 

If eccentricity of the hyperbola $\dfrac {x^{2}}{\cos^{2}\theta}-\dfrac {y^{2}}{\sin^{2}\theta}=1$ is more then $2$ when $\theta\ \in \ \left(0,\dfrac {\pi}{2}\right)$. Find the possible values of length of latus rectum 

The latus rectum of the hyperbola $16{x^2} - 9{y^2} = 144$ is-

The Vertex of the parabola $y^{2} - 10y + x + 22=0$ is.

The centre of the hyperbola 9x$^2$ - 36 x - 16y$^2$ + 96y - 252 = 0 is

Find the locus of a point which moves so that the difference of its distances from the points, $(5, 0)$ and $(-5, 0)$ is $2$ is:

If $e$ and $e'$ be the eccentricities of two conics $S$ and $S'$ such that $\displaystyle e^{2}+(e')^{2}= 3,$  then both $S$ and $S'$ are