7.4 Hyperbolas practice 2

Consider the hyperbola with equation [math]\dfrac{(y-3)^2}{20}-\dfrac{(x+1)^2}{5}=1[/math]. Let [math]d[/math] be the [math]y[/math]-intercept of the asymptote with a positive slope. Let [math]g[/math] be the sum of the [math]y[/math]-coordinates of the foci. Evaluate [math]\mid d-g \mid[/math].

The equation [math]4x^2-y^2-24x+4y-32=0[/math] represents a conic section. Find the distance between the foci.

Write the equations of the asymptotes for the hyperbola [math]\dfrac{y^2}{49}-\dfrac{x^2}{9}=1[/math].

The slope of the asymptotes of the hyperbola [math]\dfrac{x^2}{4}-\dfrac{y^2}{3}=1[/math]

Identify the graph of [math]\dfrac{(x-3)^2}{2}-\dfrac{(y+1)^2}{9}=1[/math]

Find the standard form of the equation for the hyperbola with center [math](0,-2)[/math], one vertex [math](0,-4)[/math], and one focus [math](0,2)[/math].