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Equations of Hyperbolas

HSG-GPE.A.3
Answer Keys Here

Aligned To Common Core Standard:

Expressing Properties - HSG-GPE.A.3

How to find the Equation of a Hyperbola? In analytic geometry, there are several different types of curves, and the most common ones include hyperbolas and ellipses. Hyperbola is a smooth curve lying in a plane. When a right circular cone intersects with a plane at a specified angle, which cuts both halves of the cone, it produces two unbounded curves, which we call the hyperbolas. Both curves are a reflection of each other and are not connected. A hyperbola may occur vertically or horizontally; horizontal: (x-h)2/a2 - (y-k)2/b2 =1, vertical: (y-k) 2/a2 -(x-h)2/b2 =1 These are the two patterns of a hyperbola, and you can determine the equation of a hyperbola using these patterns. These are used when the center is not the origin. When the origin is the center, the pattern becomes; horizontal: x2/a2 -y2/b2 =1, vertical: y2/a2 -x2/b2 =1 Here, (h,k) are the coordinates of the center point. (±a,0) are the vertices. (0,±b) are the coordinates of co-vertices. a and b are connected via the formula, c2=a2+b2 (±c,0) are the coordinates of the foci. The distance between two vertices is equal to 2a. The center can be calculated using the midpoint formula using the two vertices. Midpoint=((x1+x2) / 2 ,(y1 + y2)/2) Distance between the center and the focus is given by ae. e here is the eccentricity. By substituting all these values in the equation, you can get the equation of a hyperbola. This series of worksheets and lessons will help students learn to write and understand equations for hyperbolas.

Printable Worksheets And Lessons




Homework Sheets

Given a few measures and location, we want you to find the equation of the hyperbolas for us.

  • Homework 1 - The point that the hyperbola is focused (pointed) on is referred to as the center.
  • Homework 2 - When we use a coordinate system, the recognizable point that is on the branch closest to the center of the hyperbola is called the vertex.
  • Homework 3 - The foci reside inside each branch of the hyperbola.



Practice Worksheets

These sheets get progressively harder.

  • Practice 1 - Find an equation of the hyperbola with x-intercepts at x = –12 and x =6, and foci at (–16, 0) and (10, 0).
  • Practice 2 - If we look at the foci, we will see that they are side-by-side. This indicates that branches of the hyperbola follow this lead. This also means that the center, foci, and vertices are on a line that is parallel to the x-axis.
  • Practice 3 - The center resides on the x-axis. This means that the xintercepts have to also be vertices for the hyperbola.



Math Skill Quizzes

If you handled the homework and practice in stride, these are pretty straight forward for you.

  • Quiz 1 - Find an equation for the hyperbola with the center at (4, 14), vertex at (0, 14), and focus at (18, 14).
  • Quiz 2 - The center is in the middle of the foci.
  • Quiz 3 - Write the standard equation of each Hyperbola: x2 / 9 – (y+4)2 / 36 = 1