Tag: hyperbola
Questions Related to hyperbola
If $x + 2 = 0$ and $y = 1$ are the equation of asymptotes of rectangular hyperbola passing through (1,0).Then which of the following is(are) not the equation(s) of hyperbola :
If ax + by + c = 0 and $\displaystyle \varphi \chi $ + my + n = 0 are asymptotes of a hyperbola, then:
If $\theta$ is the angle between the asymptotes of the hyperbola $\displaystyle \frac{x^2}{a^2}\, -\, \displaystyle \frac{y^2}{b^2}\, =\, 1$ with eccentricity $e$, then $\sec \displaystyle \frac{\theta}{2}$can be
The asymptotes of a hyperbola are parallel to lines $2x + 3y = 0$ and $3x + 2y = 0.$ The hyperbola has its centre at $(1, 2)$ and it passes through $(5, 3).$ Find its equation.
The asymptotes of the hyperbola $xy+3x+2y = 0$ are
Find the asymptotes of the hyperbola $2x^2\, -\, 3xy\,- \, 2y^2\, +\, 3x\,- \, y\, +\, 8\, =\, 0$. Also find the equation to the conjugate hyperbola & the equation of the principal axes of the curve.
Any straight line parallel to an asymptote of a hyperbola intersects the hyperbola at
Assertion(A): The angle between the asymptotes of $3x^{2}-y^{2}=3$ is $120^{\circ}$
Reason(R): The angle between the asymptotes of $x^{2}-y^{2}=a^{2}$ is $90^{\circ}$
If $e$ is the eccentricity of $\displaystyle \frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1$ and $\theta$ be the angle between the asymptotes then $\displaystyle \sec { \frac { \theta }{ 2 } } $ equals :
The equation of hyperbola conjugate to the hyperbola $2x^2 + 3xy - 2y^2 - 5 + 5y + 2 = 0$ is