E-L-L-I-P-S-E

How to find the perimeter of an ellipse???

#Geometry #Calculus #Ellipse

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Comments

Let the ellipse be : $\displaystyle \frac{x^2}{a^2}+\frac{y^2}{b^2} = 1$

Parametric coordinates : $\displaystyle (x,y) = (a\cos\theta,b\sin\theta)$

$ds^2 = dx^2+dy^2$

$ds^2 = \left((\frac{dx}{d\theta})^2 + (\frac{dy}{d\theta})^2\right)d\theta^2$

$ds^2 = (a^2\sin^2\theta+ b^2\cos^2\theta)d\theta^2$

$ds = \sqrt{(a^2\sin^2\theta+ b^2\cos^2\theta)}d\theta$

Integrate it from $\displaystyle 0$ to $\displaystyle 2\pi$ , and you will get the result.

Anish Puthuraya - 7 years, 2 months ago

Good luck integrating that monster.! (it hasn't been solved yet)

Anish Puthuraya - 7 years, 2 months ago

i am surprised This question came in VIT couldnt solve it maths was at a good level indeed when is urs or have u already given it