how calculate chord length of ellipse.

**ashvin123** · January 31st 2010, 08:19 PM

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 ?

**earboth** · February 1st 2010, 04:18 AM

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:

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

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

Now use the distance formula.

**ashvin123** · February 2nd 2010, 02:54 AM

Thank you.
Thank you very much.

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