An ellipse is represented parametrically by .

MATHEMATICS · Multi-part · ISC · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

An ellipse is represented parametrically by x=5cos⁡θ,  y=3sin⁡θ  (0≤θ<2π)x=5\cos\theta,\;y=3\sin\theta\;(0\le \theta<2\pi). (i) Obtain the equation of the tangent to the ellipse at the parameter value θ=π6\theta=\dfrac{\pi}{6}. (ii) Determine the points where this tangent meets the coordinate axes. (iii) Calculate the area of the triangle formed by the tangent and the two coordinate axes.

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