$\"\"$

The parametric equations of an hyperbola equation are $\"\"$ and $\"\"$ .

Eliminate the parameter $\"\"$ .

Consider $\"\"$ .

$\"\"$

Consider $\"\"$ .

$\"\"$

$\"\"$ .

Pythagorean identity: $\"\"$ .

Substitute $\"\"$ and $\"\"$ .

$\"\"$

The standard form of an hyperbola equation is $\"\"$ .

$\"\"$

The standard form of an hyperbola equation is $\"\"$ .