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Section 4.4 : Hyperbolas

For problems 1 – 3 sketch the hyperbola.

1. \( \displaystyle \frac{{{y^2}}}{{16}} - \frac{{{{\left( {x - 2} \right)}^2}}}{9} = 1\) Solution
2. \( \displaystyle \frac{{{{\left( {x + 3} \right)}^2}}}{4} - \frac{{{{\left( {y - 1} \right)}^2}}}{9} = 1\) Solution
3. \( \displaystyle 3{\left( {x - 1} \right)^2} - \frac{{{{\left( {y + 1} \right)}^2}}}{2} = 1\) Solution

For problems 4 & 5 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. \(4{x^2} - 32x - {y^2} - 4y + 24 = 0\) Solution
2. \(25{y^2} + 250y - 16{x^2} - 32x + 209 = 0\) Solution