Question

The equation of a hyperbola is 4x -(y+3) 9 a) Find the center, vertices, transverse axis, and asymptotes of the hyperbola b) Use the vertices and the asymptotes to graph the hyperbola a) The center of the hyperbola isType an ordered pair.) The vertices are Type an ordered pair. Use a comma to separate answers as needed.) The equation of the transverse axis is (Type an equation.) Determine the equations of the asymptotes. Choose the correct answer below b) Choose the correct graph below с. -8 -8

Answer 1

$\newline \vspace{0.3cm} \newline \text{Transverse axis is the line joining the foci.} \newline \textbf{Equation of the transverse axis is : }y=-3 \vspace{0.5cm} \newline \text{Equation of the asymptote of (1) is given by :} \newline y+3=\pm\frac{b}{a}(x-h) \newline y+3=\pm\frac{3}{3/2}(x-0) \newline y+3=\pm2x \newline \textbf{Hence, option B. is the correct option } \vspace{0.5cm} \newline \textbf{ B. is the correct graph.}$