The center of a hyperbola is (−4,3) , and one vertex is (−4,7) . The slope of one of the asymptotes is 2.What is the equation of the hyperbola in standard form?

Answer:The answer to your question is belowStep-by-step explanation:C (-4, 3)V (-4, 7)asymptotes = 2 = [tex]\frac{b}{a}[/tex]- This is a vertical hyperbola, the equation is        [tex]\frac{(y - k)^{2} }{a^{2} } + \frac{(x - h)^{2} }{b^{2} } = 1[/tex]slope = 2a is the distance from the center to the vertex = 4b = 2(4) = 8        [tex]\frac{(y - 3)^{2} }{4^{2} } + \frac{(x + 4)^{2} }{8^{2} } = 1[/tex]        [tex]\frac{(y - 3)^{2} }{16} + \frac{(x + 4)^{2} }{64} = 1[/tex]