Expert: Sherman D. - 8/13/2004

Question
How can we know the area of a graph -

  (x/a)^(2)  +   (y/b)^(2) = 1 is the equation of a ellipse.

Now my question is how to find the area of this ellipse. For instence the equation of a circle whose center is at the origin is
  
      x^(2)   +  y^(2)  =  r^(2)

now we can easily find the area as we now the radius (r) so by formulation of the area =
(pi) r^(2) we can get the area.

But how do we find the area of the internal part of a parabola whose equation is,

       y = ax^(2) + bx + c   

and an astroid whose equation is,

       x^(2/3)  +  y^(2/3)  =  a^(2/3)

and so on.

Answer
A = Pi(ab)

Here is what i can tell you

Coordinates

x = a
then
y = a

In

(±x,0) and (0,±y)

A parabola is half an Ellipse.

areas of a Circle are different from the Area of an Ellipse.

Found at http://mathforum.org/dr.math/faq/formulas/faq.ellipse.html

More info at http://mathforum.org/dr.math/faq/formulas/index.html