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.

153

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

168

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

165

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

201

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 $open paren 0 comma 4 close paren$ .

245

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

201

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

145

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).

348

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

202

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

477

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

549

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

314

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

247

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

202

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

236

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)

282

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)

340

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

462

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)

340

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

259

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

207

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

292

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

191

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

199

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

227

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

276

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

221

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

211

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

348