Mathematics Grade 6 15 min

Write equations of hyperbolas in standard form

Write equations of hyperbolas in standard form

What you'll learn

  • Identify the center, vertices, and foci of a hyperbola given its equation in general form, and accurately convert the equation to standard form.
  • Solve problems by writing the equation of a hyperbola in standard form given key information such as the center, vertices, foci, asymptotes, or a combination thereof, and verify the solution using graphing technology.
  • Explain the relationship between the parameters (a, b, c) in the standard form equation of a hyperbola and its graphical characteristics, including the orientation (horizontal or vertical transverse axis), and justify the reasoning using algebraic and geometric representations.
  • Apply knowledge of conic sections to solve real-world application problems involving hyperbolas, such as determining the location of a ship using LORAN (LOng RAnge Navigation) systems, by formulating and solving appropriate equations in standard form.

Tutorial Preview

1

Find the equation for a horizontal hyperbola at the origin.

2

Find the equation for a vertical hyperbola at the origin.

3

Find the equation for a shifted horizontal hyperbola.

Sample Practice Questions

Easy
Find the equation for a hyperbola with vertices at (+/-2, 0) and co-vertices at (0, +/-1).
0.x^2/4-y^2/1=1
1.y^2/4-x^2/1=1
2.x^2/1-y^2/4=1
3.x^2/4+y^2/1=1
Easy
Find the equation for a hyperbola with vertices at (0, +/-3) and co-vertices at (+/-2, 0).
0.x^2/9-y^2/4=1
1.y^2/9-x^2/4=1
2.y^2/4-x^2/9=1
3.y^2/9+x^2/4=1
Easy
Find the equation for a hyperbola with vertices at (+/-3, 0) and co-vertices at (0, +/-1).
0.x^2/9-y^2/1=1
1.y^2/9-x^2/1=1
2.x^2/1-y^2/9=1
3.x^2/9+y^2/1=1

Want to practice and check your answers?

Sign up to access all questions with instant feedback, explanations, and progress tracking.

Start Practicing Free

More from Exponents and square roots

Mathematics for other grades

Frequently asked questions

What grade level is "Write equations of hyperbolas in standard form"?

Write equations of hyperbolas in standard form is a Grade 6 Mathematics lesson on ExcelOS.

What will I learn in Write equations of hyperbolas in standard form?

You'll be able to: Identify the center, vertices, and foci of a hyperbola given its equation in general form, and accurately convert the equation to standard form; Solve problems by writing the equation of a hyperbola in standard form given key….

Is "Write equations of hyperbolas in standard form" free to practice?

Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.

How many practice questions are included with Write equations of hyperbolas in standard form?

This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.

Ready to find your learning gaps?

Take a free diagnostic test and get a personalized learning plan in minutes.