Hyperbolas
Hyperbolas
Example 3
Graph the following equation.
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.