Show All Notes Hide All Notes

Section 4.4 : Hyperbolas

For problems 1 – 5 sketch the hyperbola.

1. \( \displaystyle \frac{{{x^2}}}{9} - \frac{{{y^2}}}{4} = 1\)
2. \( \displaystyle \frac{{{{\left( {y + 3} \right)}^2}}}{{36}} - \frac{{{{\left( {x + 2} \right)}^2}}}{{16}} = 1\)
3. \( \displaystyle \frac{{{{\left( {y - 5} \right)}^2}}}{{49}} - \frac{{{x^2}}}{{64}} = 1\)
4. \( \displaystyle 9{\left( {x - 4} \right)^2} - \frac{{{{\left( {y - 1} \right)}^2}}}{4} = 1\)
5. \( \displaystyle \frac{1}{{25}}{\left( {y + 1} \right)^2} - 15{\left( {x - 3} \right)^2} = 1\)

For problems 6 – 8 complete the square on the \(x\) and \(y\) portions of the equation and write the equation into the standard form of the equation of the hyperbola.

1. \(9{x^2} - 4{y^2} + 48y - 180 = 0\)
2. \({y^2} - 6y - 4{x^2} - 8x - 11 = 0\)
3. \(7{x^2} - 28x - 4{y^2} + 40y - 100 = 0\)