Question

A hyperbola has vertices (+-3,0) and one focus (5,0). What is the standard form of the equation of the hyperbola?

Please show all steps! :)

Answer 1

Lol. :) @mathmale

Answer 2

the difference between two points, the foci, to the curve remains constant. that's a hyperbola.

in an ellipse, the sum of the distances from two points, the foci, to the curve is constant.

Answer 3

so if one focus is at (5, 0) and the two veritces (points on the hyperbola which line on a line between the two foci) are \((\pm3,0)\) you should be able to find the other focus.

also, given the def of a hyperbola, let (x, y) be a point on the hyperbola and use the definition to find the equation for it.

Answer 4

Thinking.. lol. I got this.. I think. I'm not great with math but I'm trying.