South of the White House in Washington, D.C., is the President’s Park South, or the Ellipse, which hosts events such as the White House Garden Tours. The Ellipse is 880 ft from north to south and 1057 ft from east to west. Write an equation in standard form for the Ellipse, centered at the origin.

Note: If any values of a2 or b2 are greater than 1,000, include the comma.

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29-10-2017
Mathematics

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South of the White House in Washington, D.C., is the President’s Park South, or the Ellipse, which hosts events such as the White House Garden Tours. The Ellipse is 880 ft from north to south and 1057 ft from east to west. Write an equation in standard form for the Ellipse, centered at the origin.

Note: If any values of a2 or b2 are greater than 1,000, include the comma.

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TheAtomicMerher42 TheAtomicMerher42 · Answer 1 · 2017-10-29T03:54:01+01:00

To answer this, we need to start with the standard equation for an ellipse:
(x^2/a^2)+(y^2/b^2)=1
Where a is one half of one axis, and b is one half of the other.
The problem states that one axis is 1057 ft, and the other is 880 ft, so divide these values by 2 and square them. This results in:
(x^2/279,312.25)+(y^2/193,600)=1
For verification, if you have a graphing calculator, solve for y, set the size of the window so it should perfectly fit the ellipse, and check (it does)