8. Conic Sections

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Given the hyperbola $\frac{x^{2}}{25} - \frac{y^{2}}{9} = 1$ , find the length of the $a$ -axis and the $b$ -axis.

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Given the hyperbola $x^{2} - \frac{y^{2}}{4} = 1$ , find the length of the $a$ -axis and $b$ -axis.

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Given the hyperbola $\frac{y^{2}}{100} - \frac{x^{2}}{139} = 1$ , find the length of the $a$ -axis and the $b$ -axis.

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Determine the vertices and foci of the hyperbola $\frac{y^2}{4}-x^2=1$ .

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Find the equation for a hyperbola with a center at $open paren 0 comma 0 close paren$ , focus at $open paren 0 comma negative 6 close paren$ and vertex at $open paren 0 comma 4 close paren$ .

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Find the equations for the asymptotes of the hyperbola $\frac{x^{2}}{64} - \frac{y^{2}}{100} = 1$ .

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Find the equations for the asymptotes of the hyperbola $\frac{y^{2}}{16} - \frac{x^{2}}{9} = 1$ .

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Explain why it is not possible for a hyperbola to have foci at (0,-2) and (0,2) and vertices at (0,-3) and (0,3).

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Graph the hyperbola. Locate the foci and find the equations of the asymptotes. (x^2)/16 - y^2 = 1

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Graph the hyperbola. Locate the foci and find the equations of the asymptotes. ((x-2)^2)/25 - ((y+3)^2)/16 = 1

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Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci: (-8,0), (8,0); Vertices: (-3,0), (3,0)

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Graph the hyperbola. Locate the foci and find the equations of the asymptotes. 4y^2 - x^2 = 16

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Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci: (0,-4), (0,4); Vertices: (0, -2), (0,2)

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Graph the hyperbola. Locate the foci and find the equations of the asymptotes. (x^2)/16 - y^2 = 1

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In Exercises 1–4, find the vertices and locate the foci of each hyperbola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d). y^2/4−x^2/1=1

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In Exercises 5–12, find the standard form of the equation of each hyperbola satisfying the given conditions. Foci: (0, −3), (0, 3) ; vertices: (0, −1), (0, 1)

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In Exercises 5–12, find the standard form of the equation of each hyperbola satisfying the given conditions. Foci: (−4, 0), (4, 0); vertices:(−3, 0), (3, 0)

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In Exercises 5–12, find the standard form of the equation of each hyperbola satisfying the given conditions. Endpoints of transverse axis: (0, −6), (0, 6); asymptote: y=2x

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In Exercises 5–12, find the standard form of the equation of each hyperbola satisfying the given conditions. Center: (4, −2); Focus: (7, −2); vertex: (6, −2)

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In Exercises 13–26, use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. y^2/16−x^2/36=1

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In Exercises 13–26, use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. 4y^2−x^2=1

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In Exercises 13–26, use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. 9x^2−4y^2=36

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In Exercises 27–32, find the standard form of the equation of each hyperbola.

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In Exercises 27–32, find the standard form of the equation of each hyperbola.

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In Exercises 33–42, use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. (x+4)^2/9−(y+3)^2/16=1

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In Exercises 33–42, use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. (x−3)^2−4(y+3)^2=4

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In Exercises 33–42, use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. (x−1)^2−(y−2)^2=3

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In Exercises 49–56, identify each equation without completing the square. 100x^2 - 7y^2 + 90y - 368 = 0

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Find the standard form of the equation of the hyperbola with vertices (0, −6) and (0, 6), passing through (0, 9).

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