Pre Calc Question

Question

A marketplace in Australia is in the shape of an ellipse. We can assume the center of the marketplace is at the point (0,0), the location of one of the foci is at the point 

(74,0), and the length of the minor axis is 78. Determine the location of each of the vertices of the marketplace. Assume that the major length is horizontal and round your answer to the nearest thousand if needed.

PLEASE show your work or justify your answer.

1. (77.895,0) and (−77.895,0)

1. (76.337,0) and (−76.337,0)

1. (83.648,0) and (−83.648,0)

1. (81.707,0) and (−81.707,0)

1. None of these are correct.

Answer 1

Answer 3 is correct.

In an ellipse, the foci² = major² - minor² or c² = a² - b²

In this example, c is 74, and b is 78/2 or 39 (half the minor axis length)

So, 74² = a² - 39² which gives a = 83.648, the distance from the center to the endpoint of the major axis.