Question

PLEASE HELP WILL GIVE A MEDAL
Graph the hyperbola with equation:

Answer 1

recall \(\bf \cfrac{(x-{\color{brown}{ h}})^2}{{\color{purple}{ a}}^2}-\cfrac{(y-{\color{blue}{ k}})^2}{{\color{purple}{ b}}^2}=1
\\ \quad \\
center\ ({\color{brown}{ h}},{\color{blue}{ k}})\qquad vertices\ ({\color{brown}{ h}}\pm a,{\color{blue}{ k}})\qquad co-vertices\ ({\color{brown}{ h}},{\color{blue}{ k}}\pm b)
\\ \quad \\ \quad \\
\cfrac{(x-2)^2}{9}-\cfrac{(y+1)^2}{16}=1\implies \cfrac{(x-{\color{brown}{ 2}})^2}{3^2}-\cfrac{(y-{\color{blue}{ -1}})^2}{4^2}=1\)

Answer 2

the fraction with the "positive sign", is the fraction that has the "x" in it, thus the hyperbola opesn sideways, or over the x-axis, or it has a horizontal traverse axis

Answer 3

how do i graph this though?