HEYA THE PROBLEM IS AT THE DESCRIPTION it is a pre-calculus problem thanks !!!

Question

pls tell me how to get the answer and show me the solution this is the full problem

A basketball court is inside a gymnasium whose ceiling is in semi-elliptical shape. The two rings are 90ft away from each other and standing at the foci. If the gymnasium is 118ft across, how high is the gymnasium from the center of the court?

Answer 1

Draw and label a diagram!

b represents the semi-minor axis - height of the gym

a represents the semi-major axis - half the length of the gym

c represents the foci - location of the hoops.

a² = b² + c²

Can you substitute values and answer?

Answer 2

Start by reviewing the basic equations for an ellipse:

https://en.wikipedia.org/wiki/Ellipse

The simplest standard form:

x² / a² + y² / b² = 1

For a "horizontal" ellipse, a is larger than b and a is called the "semi-major axis", and b is the "semi-minor axis".

c is the distance from the center to each focus, and c = √(a² - b² )

You are given the total width, and the distance between the foci. This allows you to calculate the semi-minor axis, which is the distance from the horizontal axis to the top.

BUT--there is an ambiguity in the problem statement: If the "rings" are at the foci, then the ellipse equation gives us the vertical distance from the rings to the top of the ellipse. To get the total height of the building, we need the height of the rings above the floor.