Asymptotes of Hyperbola

Find the equation to the hyperbola, whose asymptotes are the straight lines $3 x-4 y+7=0$, and $4 x+3 y+1=0$, and which passes through the origin. Write down also the equation to the conjugate hyperbola.

Find the asymptotes of the following hyperbola and also the equation to their conjugate hyperbola.

$19x^2+24xy+y^2-22x-6y=0$

Find the equation of a hyperbola, conjugate to the hyperbola $x^2+3xy+2y^2+2x+3y=0$.

Find the equation to the hyperbola, whose asymptotes are the straight lines $3 x-4 y+7=0$, and $4 x+3 y+1=0$, and which passes through the origin. Write down also the equation to the conjugate hyperbola.

Find the equation to the hyperbola, whose asymptotes are the straight lines $x+2y+3=0$, and $3x+4y+5=0$, and which passes through the point $\left(1,-1\right)$. Write down also the equation to the conjugate hyperbola.

Find the horizontal asymptote of the following rational function:

$f\left(x\right)=\frac{8x^2-5x+1}{4x^2-3}$

Find the horizontal asymptote of the following rational function:

$f\left(x\right)=\frac{3x^2-x+12}{2x^2-6x+7}$

Find the horizontal asymptote of the following rational function:

$f\left(x\right)=\frac{4x^2-5x}{x^2-2x+1}$

Find the vertical asymptotes of the following function

$f\left(x\right)=\frac{5+2x^2}{2-x-x^2}$

Find the horizontal and vertical asymptotes of the following function

$f\left(x\right)=\frac{(x-2)(x+3)}{(x-1)(x+2)(x-5)}$

The equation of the hyperbola whose asymptotes are the lines $3x+4y-2=0, 2x+y+1=0$ and which passes through the point $(1,1)$ is

The combined equation of the asymptotes of the hyperbola $2x^2+5xy+2y^2+4x+5y=0$ is

The product of length of perpendicular from any point on the hyperbola $x^2-y^2=16$ to is symptoes is

Asymptotes of Hyperbola $\frac{x^2}{25}-\frac{y^2}{16}=1$ are .....

Asymptotes of Hyperbola $\frac{x^2}{25}-\frac{y^2}{16}=1$ are .....

From any point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, tangents are drawn to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=2$. The area cut off by the chord of contact on the region between the asymptotes is equal to -

Find the hyperbola whose asymptotes are $2x-y=3 and 3x+y-7=0$ and which passes through the point $(1, 1)$:

Angle between the asymptotes of a hyperbola $x^2+2xy-3y^2+x+7y+9=0$ is

The product of the perpendicular from any point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ to its asymptotes is equal to

The equation of a hyperbola, conjugate to the hyperbola $x^2+3xy+2y^2+2x+3y=0$ is