Table of contents

0. Review of Algebra(0)
1. Equations & Inequalities(0)
2. Graphs of Equations(0)
3. Functions(0)
4. Polynomial Functions(0)
5. Rational Functions(0)
6. Exponential & Logarithmic Functions(0)
7. Systems of Equations & Matrices(0)
8. Conic Sections(0)
9. Sequences, Series, & Induction(0)
10. Combinatorics & Probability(0)

8. Conic Sections

Hyperbolas at the Origin

8. Conic Sections

Hyperbolas at the Origin - Online Tutor, Practice Problems & Exam Prep

Hyperbolas at the Origin Practice Problems

22 problems

Here Foci (±1, 0) and vertices (±2, 0) are given. Define the reason why it is not possible to have these foci and vertices for a hyperbola.

2PRACTICE PROBLEM

Find the equation of the asymptote and indicate the loci after graphing the hyperbola x²/25 - y² = 1

3PRACTICE PROBLEM

Find the equation of the asymptote and indicate the foci after graphing the hyperbola (x+1)²/36 - (y-2)²/64 =1

4PRACTICE PROBLEM

Consider the foci and vertices of the hyperbola given below. Determine the standard form of the equation of the hyperbola using the given information. Foci: (0, ±5) Vertices: (0, ±1)

5PRACTICE PROBLEM

Find the equation of the asymptote and indicate the loci after graphing the hyperbola 9y² - 4x² = 36

6PRACTICE PROBLEM

Consider the foci and vertices of the hyperbola given below. Determine the standard form of the hyperbola equation using the given information. Foci: (±√61, 0) Vertices: (±5, 0)

7PRACTICE PROBLEM

For the given equation, graph the hyperbola and indicate the vertices and foci.

x²/16 - y²/9 = 1

8PRACTICE PROBLEM

For the given equation, graph the hyperbola and indicate the vertices and foci.

y²/16 - x²/9 = 1

9PRACTICE PROBLEM

Given the following conditions of a hyperbola, solve for the standard form of its equation

Foci: (0, - 5), (0, 5); Vertices (0, -2), (0, 2)

10PRACTICE PROBLEM

Given the following conditions of a hyperbola, solve for the standard form of its equation.

Foci: (- 5, 0), (5, 0);
Vertices (- 1, 0), (1, 0)

11PRACTICE PROBLEM

Given the following conditions of a hyperbola, solve for the standard form of its equation

Endpoints of transverse axis: (0, - 8), (0, 8)
Asymptote: y = 4x

12PRACTICE PROBLEM

Given the following conditions of a hyperbola, solve for the standard form of its equation.

Center: (3, - 1);
Focus: (9, - 1);
Vertex: (7, - 1)

13PRACTICE PROBLEM

Graph the hyperbola defined by y²/25 - x²/64 = 1 using its vertices and asymptotes. Then, determine the equations of the asymptotes and the foci.

14PRACTICE PROBLEM

Graph the hyperbola defined by y² - 9x² = 1 using its vertices and asymptotes. Then, determine the equations of the asymptotes and the foci.

15PRACTICE PROBLEM

Graph the hyperbola defined by 4x² - 25y² = 100 using its vertices and asymptotes. Then, determine the equations of the asymptotes and the foci.

16PRACTICE PROBLEM

The graph of a hyperbola is shown. Determine the standard form of its equation.

17PRACTICE PROBLEM

The graph of a hyperbola is shown. Determine the standard form of its equation.

18PRACTICE PROBLEM

The equation of the hyperbola is given below. Draw the graph using its center, vertices, and asymptotes. Find the equations for the asymptotes and the coordinates of the foci.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfrac><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>2</mn><msup><mo>)</mo><mn>2</mn></msup></mrow><mn>25</mn></mfrac><mo>-</mo><mfrac><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>4</mn><msup><mo>)</mo><mn>2</mn></msup></mrow><mn>49</mn></mfrac><mo>=</mo><mn>1</mn></mstyle></math>","truncated":false}$

19PRACTICE PROBLEM

The equation of the hyperbola is given below. Draw the graph using its center, vertices, and asymptotes. Find the equations for the asymptotes and the coordinates of the foci.

(x + 1)² − 9(y - 2)² = 9

20PRACTICE PROBLEM

The equation of the hyperbola is given below. Draw the graph using its center, vertices, and asymptotes. Find the equations for the asymptotes and the coordinates of the foci.

(x + 3)² − (y + 5)² = 5

21PRACTICE PROBLEM

Without completing the square, determine the given equation.
25x² - 78y² + 16y -112= 0

22PRACTICE PROBLEM

Work out the standard form of the hyperbola equation, given the following conditions.

Vertices: (0, - 9) and (0, 9)
Passes through the point: (9, 6)