Question

Part 4: model a real world problem using an ellipse

Answer 1

a. The equation of the ellipse is x²/900 + y²/400 = 1

b. the foci of the ellipse are at (±10√5,0)

c. Find the graph in the attachment

How to find the equation of the ellipse?

Since the ellipse is made from a block of wood and centered at the origin, and x- axis major axis.

So, the equation of an ellipse with center at origin and x - axis major axis is

x²/a² + y²/b² = 1 where

• 2a = length of major axis
• 2b = length of minor axis and
• a > b

Since the rectangular piece of wood  has a length of 60 inches and a width of 40 inches.

The length of the rectangle equals the length of the major axis

So, 2a = 60

a = 60/2

= 30

Also, the width of the rectangle equals the length of the minor axis

So, 2b = 40

b = 40/2

= 20

a. The equation of the ellipse

So, substituting a and b into the equation of the ellipse, we have

x²/a² + y²/b² = 1

x²/30² + y²/20² = 1

x²/900 + y²/400 = 1

So, the equation of the ellipse is x²/900 + y²/400 = 1

b. The foci of the ellipse

The foci of the ellipse are at (±c,0) where c² = a² - b²

= 30² - 20²

= 900 - 400

= 500

c = ±√500

c = ±10√5

So, the foci of the ellipse are at (±10√5,0)

c. Find the graph in the attachment

Learn more about equation of ellipse here:

brainly.com/question/1687265

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