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For the standard ellipse, perpendiculars are dropped from the centre to the tangent and to the normal at the point whose eccentric angle is pi/4. Find the area of the rectangle formed by these two perpendiculars.

1. ((a² - b²)*a*b)/(a² + b²)
2. ((a² - b²))/((a² + b²)*a*b)
3. ((a² - b²))/(a*b*(a² + b²))
4. ((a² + b²))/((a² - b²)*a*b)

Correct answer: ((a² - b²)*a*b)/(a² + b²)

Solution

Computing the perpendicular distances from the centre to the tangent and normal at theta = pi/4 and multiplying yields ((a² - b²)*a*b)/(a² + b²).

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