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# What is the equation for this problem?

The design for a new park is in the shape of an ellipse. The park is to be 3,000 yards long and 1,300 yards wide. With the center of the park at the origin, write an equation to represent the shape of the park.

### 2 Answers

- PuzzlingLv 72 months agoFavorite Answer
For an ellipse centered at the origin with its major axis on the y-axis:

x²/b² + y²/a² = 1

a --> length of the semi-major axis (half the longer axis) --> 3000/2 = 1500

b --> length of the semi-minor axis (half the shorter axis) --> 1300/2 = 650

Answer:

x²/650² + y²/1500² = 1

Take a look at the graph below.

P.S. If the graph were wider along the horizontal axis, you'd reverse the positions of a and b.

Source(s): https://www.desmos.com/calculator/ahge382wn3