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04/01/2022 1:06 pm
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If \(\frac{x^2}{b^2}\) + \(\frac{y^2}{4a^2}\) = 1 and minimum area with coordinate axes of tangent is Kab, then the value of K is.
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04/01/2022 1:10 pm
\(\frac{x^2}{b^2}\) + \(\frac{y^2}{4a^2}\) = 1
Equation of tangent is \(\frac{x}{b}\)cosθ + \(\frac{y}{2a}\) sin θ = 1
Area(ΔOAb) = \(\frac{1}{2}\)(2ab)(secθ csc θ)
Area = \(\frac{2ab}{sin 2 \theta}\)
Minimum area = 2ab (Therefore, θ = 45 degrees)
So, K = 2