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Properties of an Ellipse

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Equation: x^2+9y^2-4x+54y+49=0

1. Identify the conic section represented by the equation.

2. Write the equation of the conic section in standard form.

3. Identify relevant key elements of your conic section such as center, focus/foci, directrix, radius, lengths of major and and or minor axes, equations of asymptotes, and length of latus rectum. (Note: not all key elements apply to each equation.)

4. Determine the equation of the line that is tangent to the conic section at the point: (34/5, -9/5)

Solution Summary

This problem demonstrates how to write the equation of an ellipse in standard form and how to find certain properties of the conic section such as the center, major and minor axes, directrix, etc. The slope of a tangent line to the ellipse is found through the method of derivatives.

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