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.

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

Find the equation of the ellipse with the following properties. Express your answer in standard form.

Major axis vertical length = 14; length of minor axis = 6; center: (-1, 2)

The following equation is that of a parabola. Using its vertex and the direction in which it opens, solve for its domain and range, and tell if the given relation is a function or not.

y² + 4y - x - 3 = 0

Draw the parabola on the coordinate system after finding the vertex, focus, and directrix of the parabola. (x+2)²= 4(y-2)

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.

Find the equation of the asymptote and indicate the foci after graphing the hyperbola (x+1)²/36 - (y-2)²/64 =1

The graph of a hyperbola is shown. Determine the standard form of its equation.