Derivation of condition for three ellipse to have a common tangent.
ikshit jalan , 8 Years ago
Grade 12th pass
Analytical Geometry> Derivation of condition for three ellipse...
1 Answers
Vikas TU
Last Activity: 8 Years ago
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
b2 /a2 = d2 / c2 = f2 / e2 .
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