Hyperbolas

Hyperbolas

Example 3

Graph the following equation.

HyperbolasEx3-1

Step 1 . Identify the conic section.

This is a hyperbola because the x and y terms are both squared and the y term is subtracted from the x term, creating a horizontal transverse axis.

Step 2 . Identify the center, vertices, and the corners of the rectangle.

Center: (2, ?3)

Vertices: (2 + 4, -3) and (2 - 4, -3) or (6, -3) and (-2, -3)

Coordinates of the corners of the rectangle:
  • (2 + 4, -3 + 5) = (6, 2)
  • (2 - 4, -3 + 5) = (-2, 2)
  • (2 + 4, -3 - 5) = (6, -8)
  • (2 - 4, -3 - 5) = (-2, -8)
Step 3 . Graph the conic.

HyperbolasEx3-2