11.4 Hyperbolas

Before you get started, take this readiness quiz.

Solve: $x^{2} = 12 .$
If you missed this problem, review the reference.

Expand: $\left(x - 4\right)^{2} .$
If you missed this problem, review the reference.

Identify the graph of each equation as a circle, parabola, ellipse, or hyperbola.

ⓐ $9 x^{2} + 4 y^{2} + 56 y + 160 = 0$ ⓑ $9 x^{2} - 16 y^{2} + 18 x + 64 y - 199 = 0$ ⓒ $x^{2} + y^{2} - 6 x - 8 y = 0$ ⓓ $y = −2 x^{2} - 4 x - 5$

Identify the graph of each equation as a circle, parabola, ellipse, or hyperbola.

ⓐ $x^{2} + y^{2} - 8 x - 6 y = 0$ ⓑ $4 x^{2} + 25 y^{2} = 100$ ⓒ $y = 6 x^{2} + 2 x - 1$ ⓓ $16 y^{2} - 9 x^{2} = 144$

Identify the graph of each equation as a circle, parabola, ellipse, or hyperbola.

ⓐ $16 x^{2} + 9 y^{2} = 144$ ⓑ $y = 2 x^{2} + 4 x + 6$ ⓒ $x^{2} + y^{2} + 2 x + 6 y + 9 = 0$ ⓓ $4 x^{2} - 16 y^{2} = 64$

Identify the type of graph.

ⓐ $x = −2 y^{2} - 12 y - 16$ ⓑ $x^{2} + y^{2} = 9$ ⓒ $16 x^{2} - 4 y^{2} + 64 x - 24 y - 36 = 0$ ⓓ $16 x^{2} + 36 y^{2} = 576$

Explain in your own words how to create and use the rectangle that helps graph a hyperbola.

Explain in your own words, how to distinguish the equation of an ellipse with the equation of a hyperbola.