Question

This hyperbola is centered at the origin. Find its equation.

Answer 1

Step-by-step explanation:

Use these equations.

Equation of a Hyperbola, centered at orgin

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

where a is the major axis

B is the minor axis.

Since a and X are first, the x axis is the major.

This also means the x axis contains the vertices and foci as well.

The equation of vertices when x is major axis is

$(x ±a)$

Since the vertices are (±1,0), and the orgin is (0,0). The length of a is 1.

So a=1.

The equation of foci is

$(x±c)$

Where c is formed by

${c}^{2} = {a}^{2} + {b}^{2}$

We know that c is 2 since the distance from the foci and center is 2. A is 1, so let find b.

${2}^{2} = {1}^{2} + {b}^{2}$

$4 = 1 + {b}^{2}$

$3 = {b}^{2}$

$\sqrt{3} = {b}$

So our equation is

$\frac{ {x}^{2} }{1 {}^{2} } - \frac{ {y}^{2} }{ (\sqrt{3}) {}^{2} } = 1$

$\frac{ {x}^{2} }{1} - \frac{ {y}^{2} }{3} = 1$