The minimum distance between conic 'C' and ellipse E is

Engineering

Mathematics

Standard Ellipse

Question

$\frac{3}{2}$

$\frac{5}{2}$

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$Let point on \frac{x^{2}}{9} + \frac{y^{2}}{4} = 1 is (3 \cos θ, 2 \sin θ)$

C.O.C. of x² + y² =1 is 3x cos θ + 2y sin θ = 1
and C.O.C. is always tangent to 9x² + 4y² = 1.

$Hence, conic ' C^{'} is \frac{x^{2}}{\frac{1}{9}} + \frac{y^{2}}{\frac{1}{4}} = 1$

$e = \sqrt{1 - \frac{\frac{1}{9}}{\frac{1}{4}}} = \frac{\sqrt{5}}{3}$

Minimum distance between conic C and ellipse E is $B_{1} D_{1} = \frac{3}{2}$