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.

127

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

138

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

137

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

164

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 $open paren 0 comma 4 close paren$ .

199

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

153

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

126

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).

301

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

180

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

388

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

470

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

250

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

214

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

180

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

202

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)

246

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)

285

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

405

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)

301

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

215

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

181

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

236

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

154

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

167

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

186

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

229

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

174

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

190

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

271