How do you write the equation for a hyperbola given vertices (0,-4) and (0,4), conjugate axis of lengths 14 units?

1 Answer
Shwetank Mauria
Jun 30, 2017

Equation of hyperbola is y^2/16-x^2/49=1

Explanation:

As the vertices are (0,-4) and (0,4) i.e. along y-axis, we have a vertical hyperbola and equation of hyperbola is of the type

(y-k)^2/a^2-(x-h)^2/b^2=1, where (h,k) is center of hyperbola and b>a

As both vertices are equidistant from origin, center of hyperbola is (0,0) and the equation is

y^2/4^2-x^2/b^2=1

Further as length of conjugate axis is 14, we have b=14/2-7

and hence equation of hyperbola is y^2/16-x^2/49=1
graph{y^2/16-x^2/49=1 [-20, 20, -10, 10]}

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