Derivation of condition for three ellipse to have a common tangent.

Question

Vikas TU · Answer

Let the equation of 3 ellipse be x^2 / a^2 + y^2 / b^2 = 1----------------------------1 x^2 / c^2 + y^2 / d^2 = 1-----------------------------2 x^2 / e^2 + y^2 / f^2 = 1------------------------------3 Differentiate 1,2,3 w.r.t x Differentiation of (1) is - b^2 x / a^2 y-----------------------4 Differentiation of (2) is - d^2 x / c^2 y-------------------------5 Differentiation of (3) is - f^2 x / e^2 y---------------------6 For ellipse to have common tangent 4,5,6 should be equal to each other Hence b 2 /a 2 = d 2 / c 2 = f 2 / e 2 .

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Derivation of condition for three ellipse to have a common tangent.

Derivation of condition for three ellipse to have a common tangent.

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