Question

write the equation of the hyperbola with the given foci and vertices.
Foci(+-17,0) ; Vertices (+-8,0)
will give medal

Answer 1

Given these vertices this is an 'East-West opening' hyperbola. See https://en.wikipedia.org/wiki/Hyperbola. Conventionally, we use \[a\] for the distance between the y-axis and one of the vertices, \[b\]for the perpendicular distance between an asymptote and the nearest vertex and \[c\]for the distance between the y-axis and one of the foci. We know that \[a ^{2} + b ^{2} = c ^{2}\]

The equation fo an 'East-West opening' hyperbola is \[\frac{ x ^{2} }{ a ^{2} } - \frac{ y ^{2} }{ b ^{2} } = 1\]

So, you have been given c and a, and you can calculate b. It's just a matter of shoving those values into the general equation.