posted by Priscilla on .
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
(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.
what is <mnp=60 degrees