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In Figure, AOBA is the part of the elli...

In Figure, AOBA is the part of the ellipse `9x^2+y^2=36`in the first quadrant such that `O A = 2 a n d O B = 6`. Find the area between the arc AB and the chord AB.

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To solve the problem of finding the area between the arc AB and the chord AB for the ellipse given by the equation \(9x^2 + y^2 = 36\) in the first quadrant, we can follow these steps: ### Step 1: Identify the ellipse parameters The equation of the ellipse can be rewritten in standard form: \[ \frac{x^2}{4} + \frac{y^2}{36} = 1 \] From this, we can identify \(a^2 = 4\) and \(b^2 = 36\), which gives us \(a = 2\) and \(b = 6\). ...
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