Posted by **Priscilla** on Friday, April 10, 2009 at 7:22pm.

The area of an ellipse in the form (x*x/a*a)+(y*y)/(b*b)=1 is A=3.14*ab. For this ellipse, a+b=20.

a. write the area of the ellipse as a function of a.

b. Find the equation of the ellipse with an area of 264 square centimeters.

c. Complete the table and make a conjecture about the shape of the ellipse with a maximum area.

a 7 8 10 11 12 13 14

b

area

- geometry -
**drwls**, Friday, April 10, 2009 at 8:05pm
(a) The area of an ellipse is

A = pi*a*b.

In this case,

A = pi * a * (20 - a)

(b) Set A = 264 and solve for a. Than use a+b=20. to get b, Then write the equation

(c) Complete the table using a+b=20. If a = 7, b = 13.

See which combination of a and b gives you a maximum value of a*b, and therefore of the area. I suspect it will be a = b = 10

This is work you should be able to do yourself.

- geometry -
**madilene**, Saturday, February 6, 2010 at 12:51am
what is <mnp=60 degrees

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