Graph the given ellipse and indicate its foci.

For the following equation of a parabola, solve for the focus and directrix, and then graph.

x² = 24y

Consider the foci and vertices of the hyperbola given below. Determine the standard form of the equation of the hyperbola using the given information. Foci: (0, ±5) Vertices: (0, ±1)

Given the following conditions of a hyperbola, solve for the standard form of its equation

Endpoints of transverse axis: (0, - 8), (0, 8)
Asymptote: y = 4x

Find the equation of the asymptote and indicate the loci after graphing the hyperbola x²/25 - y² = 1

The equation of the hyperbola is given below. Draw the graph using its center, vertices, and asymptotes. Find the equations for the asymptotes and the coordinates of the foci.

(x + 3)² − (y + 5)² = 5

Without completing the square, determine whether the equation represents a parabola, circle, ellipse, or hyperbola.

$x^2+9y^2-28x-270y+2185=0$

Determine the graph that the equation represents.

$4x^2+64x+4y^2-48y=500$