Question

A hyperbola has its center at (0,0), a vertex of (20,0 and an asymptote of y= 13/20x. find the equation that describes the hyberbola

Answer 1

Answer:

$\frac{x^2}{20^2} -\frac{y^2}{13^2} =1$

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

$\frac{x^2}{20^2} -\frac{y^2}{b^2} =1$

Asymptotes would be

$\frac{x^2}{20^2} -\frac{y^2}{b^2} =0$

Or y=bx/20

Comparing with given equation we get b =13

Hence asymptote would have equation as

$\frac{x^2}{20^2} -\frac{y^2}{13^2} =1\\\frac{x^2}{400} -\frac{y^2}{169} =1$