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Question Number 39349 by ajfour last updated on 05/Jul/18

Commented by MrW3 last updated on 08/Jul/18

$$Findtheradiusofcirclewhich$$$$dividestheperimeteroftheellipse$$$$into4equalsegments.$$

Answered by MrW3 last updated on 05/Jul/18

$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$$$\Rightarrow \frac{{\left(r\cos \theta \right)}^2}{a^2}+\frac{{\left(r\sin \theta \right)}^2}{b^2}=1$$$$\Rightarrow r\left(\theta \right)=\frac{ab}{\sqrt{{\left(a\sin \theta \right)}^2+{\left(b\cos \theta \right)}^2}}$$$$$$$$Radiusofcircle:$$$$R=r\left(\frac{\pi }{4}\right)=\frac{\sqrt{2}ab}{\sqrt{a^2+b^2}}$$

Commented by ajfour last updated on 05/Jul/18

$$ThankyouSir!$$

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