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Section 4.3 : Ellipses
For problems 1 – 3 sketch the ellipse.
- \( \displaystyle \frac{{{{\left( {x + 3} \right)}^2}}}{9} + \frac{{{{\left( {y - 5} \right)}^2}}}{3} = 1\) Solution
- \( \displaystyle {x^2} + \frac{{{{\left( {y - 1} \right)}^2}}}{4} = 1\) Solution
- \( \displaystyle 4{\left( {x + 2} \right)^2} + \frac{{{{\left( {y + 4} \right)}^2}}}{4} = 1\) 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 ellipse.