Posted by alysa on Monday, January 21, 2013 at 2:29am.
What a nasty question.
the area of the ellipse is abπ , where a and b are each 1/2 of the axes
so abπ = 12π --->ab = 6 or b = 6/a
let A(a,0) and B(0,b) be the two adjacent vertices
given AB = 5
√(a^2 + b^2) = 5
a^2 + b^2 = 25
a^2 + 36/a^2 = 25
a^4 + 36 = 25a^2
a^4 - 25a^2 + 36 = 0
a^2 = (25 ± √481)/2 = appr 23.4658 or appr 1.53414
a = 4.844157.. or a = 1.2386... ignoring the 2 negative values
then b = 6/a
if a = 4.844148, then b = 1.2386
if a = 1.2386 , then a = 4.844157
ahhh, summetrical answers
So we basically have the same ellipse, one horizontal, one vertical
The perimeter of an ellipse is one of the most challenging questions dealing with the ellipse.
It requires Calculus and finding the length of a curve.
Here is a link that has some approximation methods
Here is an applet that let's you find all properties of an ellipse
enter the 2a= 9.6883
enter 2b = 2.47721..
and press calculate to get a perimeter of appr. 20.87
2nd grade math - If you have a rectangle with 24 square units 3 lines down 8 ...
Algebra 2 - Choose the equation that best represents an ellipse for the given ...
geometry - The area of an ellipse in the form (x*x/a*a)+(y*y)/(b*b)=1 is A=3.14*...
solid mensuration - A circle has an area equal to 25 pi sq.cm. Its diameter AB ...
solid mensuration - Find the area of a portion of a semicircle of radius 15 m ...
math - square x has an area of 100 square units. Square Y has a perimeter that ...
math - one of the two numbers that can be both the perimeter and the area of the...
Calculus - I seriously do not understand anything about this problem Please ...
Algebra 1 - A circle is inscribed in a square. The number of square units in the...
Algebra 1: Help Please URGENT! - A circle is inscribed in a square. The number ...
For Further Reading