# how calculate chord length of ellipse.

• Jan 31st 2010, 08:19 PM
ashvin123
how calculate chord length of ellipse.
An ellipse
major axis: 900
minor axis: 450
Two points on ellipse 150 and 250 distance
away from center line as shown in attached file (chord length)
Then how to measure the lenght of chord AB as shown in
attached file ?
• Feb 1st 2010, 04:18 AM
earboth
Quote:

Originally Posted by ashvin123
An ellipse
major axis: 900
minor axis: 450
Two points on ellipse 150 and 250 distance
away from center line as shown in attached file (chord length)
Then how to measure the lenght of chord AB as shown in
attached file ?

If you are allowed to use a convenient coordinate system you can calculate the coordinates of the points A and B. Afterwards use the distance formula.

Put the origin of the coordinate system on the center of the ellipse. The equation of the ellipse becomes:

$\displaystyle \dfrac{x^2}{450^2} + \dfrac{y^2}{225^2}=1$

Plug in x = 150 to get $\displaystyle y = 150 \sqrt{2}$ .
Thus $\displaystyle A(150, 150\sqrt{2})$ and $\displaystyle B(250, 50 \sqrt{14})$

Now use the distance formula.
• Feb 2nd 2010, 02:54 AM
ashvin123
Thank you.
Thank you very much.