Answer:
[tex]\frac{x^2}{20^2} -\frac{y^2}{13^2} =1[/tex]
Step-by-step explanation:
Given that a hyperbola has its centre at (0,0)
Asymptote = y =13x/20
Vertex is on x axis thus a =20
Hence hyperbola will have equation as
[tex]\frac{x^2}{20^2} -\frac{y^2}{b^2} =1[/tex]
Asymptotes would be
[tex]\frac{x^2}{20^2} -\frac{y^2}{b^2} =0[/tex]
Or y=bx/20
Comparing with given equation we get b =13
Hence asymptote would have equation as
[tex]\frac{x^2}{20^2} -\frac{y^2}{13^2} =1\\\frac{x^2}{400} -\frac{y^2}{169} =1[/tex]
