Question

Write the equation of a hyperbola with vertices (-5, 0) and (5, 0) and co-vertices at (0, -6) and (0, 6)?

Answer 1

get the "a" and "b" components firstly

then plug them in

keep in mind that, the vertices are at 5,0 and -5,0, so it opens horizontally, meaning
the fraction with the "x" variable has the "a" component, that is \(\bf \cfrac{(x-{\color{brown}{ h}})^2}{{\color{purple}{ a}}^2}-\cfrac{(y-{\color{blue}{ k}})^2}{{\color{purple}{ b}}^2}=1
\qquad center\ ({\color{brown}{ h}},{\color{blue}{ k}})\qquad
vertices\ ({\color{brown}{ h}}\pm a, {\color{blue}{ k}})\)