Writing Equations of Hyperbolas Centered at the Origin Practice

1. A hyperbola centered at the origin has vertices at ‍$(\pm \sqrt{45},0)$ and foci at ‍$(\pm \sqrt{70},0)$.

   Write the equation of this hyperbola.

2. Write the equation of the hyperbola graphed below, whose vertices and foci are marked.

   
   

3. A hyperbola centered at the origin has vertices at ‍$(0,\pm \sqrt{12})$ and foci at ‍$(0,\pm \sqrt{45})$.

   Write the equation of this hyperbola.

4. Write the equation of the hyperbola graphed below, whose vertices and foci are marked.

   
   

Source: Khan Academy, https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:hyperb-foci/e/equation_of_a_hyperbola
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