JEE Delight | Maximum length of the common tangent of an ellipse and a variable circle

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JEE Delight | Ellipse & Circle | Maximum length of the common tangent of an ellipse 4x^2+and16y^2=64 and a variable circle x^2+y^2=r^2

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A much better method would be to join origin to point of tangency of circle, and complete a rectangle.
Then we observe that the required length is simply the distance of origin from normal to ellipse.
So just write eqn of normal in general form, find distance of origin from this normal, and maximize it.

iitjeemathspro
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Just take parametric coordinates ..8 lines m ho jaayega

eyepradeepin
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Amazing one sir🙏🏻, was able to solve it, but slightly differently than yours sir.
Thank you

AnshPl
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Sir pls start a complete series of isi cmi course that will be help ful

wolverines
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Sir can you please start question series for jee advanced from foreign author Book which is jee relevant??

ranbirchauhan