8. Conic Sections

Showing 5 of 5 videos

Practice this topic

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

138

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

153

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

148

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

185

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 $open paren 0 comma 4 close paren$ .

222

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

176

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

135

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).

316

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

188

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

418

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

501

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

277

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

227

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

188

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

216

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)

258

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)

303

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

432

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)

321

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

231

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

188

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

255

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

164

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

177

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

200

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

247

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

189

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

199

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

303