# Help checking whether this is right

• April 8th 2009, 08:19 AM
dan03uk
Help checking whether this is right
Hi,

I am currently trying to find the area of segment of an elipse, I know the area of the segment for the circle related to the elleipse. So all i need to do is times the area of the circle segment by (b/a).

The problem I have is that I don't know b. Am i right in thinking that if I know some points on the ellipse that I can rearange the forumal of ellipse to this:

$\frac{-\frac{x^{2}}{a^{2}}+1}{y^{2}}=b^{2}$

Sorry its all so long winded
• April 8th 2009, 11:33 AM
earboth
Quote:

Originally Posted by dan03uk
Hi,

I am currently trying to find the area of segment of an elipse, I know the area of the segment for the circle related to the elleipse. So all i need to do is times the area of the circle segment by (b/a).

The problem I have is that I don't know b. Am i right in thinking that if I know some points on the ellipse that I can rearange the forumal of ellipse to this:

$\frac{-\frac{x^{2}}{a^{2}}+1}{y^{2}}=b^{2}$......No
Sorry its all so long winded

Unfortunately you calculated $\dfrac1{b^2}$

If the center of the ellipse is at the origin the equation of the ellipse is

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1~\implies~\dfra c{y^2}{b^2}=1 - \dfrac{x^2}{a^2} = \dfrac{a^2-x^2}{a^2}$

Now calculate the reciprocals on both sides of the equation:

$\dfrac{b^2}{y^2}=\dfrac{a^2}{a^2-x^2}~\implies~\boxed{b^2=\dfrac{a^2 y^2}{a^2-x^2}}$