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Rewrite the equation of the hyperbola in standard form.

16 x ^{ 2 } – 4 y ^{ 2 } = 64

Rewrite the equation of the hyperbola in the standard form.

100 y ^{ 2 } – 9 x ^{ 2 } = 25

y ^{ 2 } – 9 x ^{ 2 } = 36

Calculate the vertices and foci of the hyperbola.

Determine the vertices and foci of the hyperbola:

Rewrite the equation in standard form. Determine the foci and vertices.

4 x ^{ 2 } – 25 y ^{ 2 } = 100

Rewrite the equation in standard form. Identify the vertices and foci of the hyperbola.

49 y ^{ 2 } – 16 x ^{ 2 } = 784

Graph the equation and identify the foci and asymptotes:

Graph the equation 100 x ^{ 2 } – 64 y ^{ 2 } = 6400 and identify the foci and asymptotes.

Graph the equation: x ^{ 2 } + y ^{ 2 } = 20

Graph the equation: x ^{ 2 } = 25 y

Graph the hyperbola:

Graph the inequality y ^{ 2 } – x ^{ 2 } 9

Graph the inequality

Find an equation of the hyperbola with the given foci and vertices.

Foci: (–10, 0), (10, 0), Vertices: (–9, 0), (9, 0)

Foci: (0, –16), (0, 16), Vertices: (0, –7), (0, 7)

Write an equation of the parabola, given:

Center: (0, 0)

Foci: (–5, 0), (5, 0)

Vertices: (–2, 0), (2, 0)

An equation for a hyperbola is given. Obtain two points on the curve with x –coordinate equal to 4.

Find the asymptotes of the parabola:

Sketch its graph.

Determine the foci of the hyperbola whose:

Asymptotes: y = 5 x , y = –5 x

A hyperbola with endpoints of the transverse axis at (–3, 0) and (3, 0) is centered at the origin. The square of the distance from the center to a focus is 45. Find an equation and graph the hyperbola.

Identify the common features of the given hyperbolas.

And also identify in what way does the given hyperbolas differ .

The coordinates of foci and the difference of focal radii are given. Use the definition of hyperbola and find the equation.

Foci: (–4, 0) and (4, 0)

Difference of focal radii = 4