# Equation of an Ellipse, Compounding Interest

1. An employee of the National Parks Service told you about a location in Washington, DC. It is a large grassy area south of the White House known as the Ellipse. The National Tree Lighting Ceremony is held annually on the Ellipse. Because the President officiates at this event, the Secret Service makes calculations which they use in planning security.

The Ellipse is actually an ellipse with major axis of length 1048 ft. and minor axis of length 898 ft. Assuming that a coordinate system is superimposed on the area in such a way that the center is at the origin and the major and minor axes are on the x- and y- axes of the coordinate system, respectively, find an equation of the ellipse.

2. The Board of Governors at the Federal Reserve Bank set the prime interest rate. These rates trickle down through the economy at various rates and affect consumer spending and saving habits. The economists at the Federal Reserve follow sample households in order to extrapolate information which they use in forecasting. For example, in one household they studied, the family made an investment for 1 year that earned $7.50 simple interest. If the principal had been $25 more and the interest rate 1% less, the interest would have been the same. Find the principal and the rate.

Among the professionals you have interviewed for your article, were several state and federal government spokespersons who use linear equations in a variety of ways.

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#### Solution Preview

1. The Ellipse is actually an ellipse with major axis of length 1048 ft. and minor axis of length 898 ft. Assuming that a coordinate system is superimposed on the area in such a way that the center is at the origin and the major and minor axes are on the x- and y- axes of the coordinate system, respectively, find an equation of the ellipse.

Equation of an ellipse is: x^2/a^2 + y^2/b^2 = 1

The length of the major axis is 2a, and the length of the minor axis is ...

#### Solution Summary

The Equation of an Ellipse and Compounding Interest are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.