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Section 4.3 : Ellipses

For problems 1 – 3 sketch the ellipse.

1. \( \displaystyle \frac{{{{\left( {x + 3} \right)}^2}}}{9} + \frac{{{{\left( {y - 5} \right)}^2}}}{3} = 1\) Solution
2. \( \displaystyle {x^2} + \frac{{{{\left( {y - 1} \right)}^2}}}{4} = 1\) Solution
3. \( \displaystyle 4{\left( {x + 2} \right)^2} + \frac{{{{\left( {y + 4} \right)}^2}}}{4} = 1\) 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.

1. \({x^2} + 8x + 3{y^2} - 6y + 7 = 0\) Solution
2. \(9{x^2} + 126x + 4{y^2} - 32y + 469 = 0\) Solution