Question

What is the equation of a hyperbola with a = 5 and c = 15? Assume that the transverse axis is horizontal.

Answer 1

`(x^2)/(25) -(y^2)/(200) =1`

Explanation:

Recall that the equation of hyperbola centered at the origin with transverse horizontal axis has the general form:

`(x^2)/(a^2) -(y^2)/(b^2) =1\\and\,\,\,\, with\\c=√(a^2+b^2)`

since we know that a = 5 ,and c = 15,we can solve for b:

`15=√(5^2+b^2) \\15^2=25+b^2\\b^2=200\\`

then the equation of the hyperbola becomes:

`(x^2)/(5^2) -(y^2)/(200) =1\\(x^2)/(25) -(y^2)/(200) =1`