Mathematics

Problem

An ellipse is represented parametrically by

x=5\cos\theta,\;y=3\sin\theta\;(0\le \theta<2\pi)

. a. (i) Obtain the equation of the tangent to the ellipse at the parameter value

\theta=\dfrac{\pi}{6}

. b. (ii) Determine the points where this tangent meets the coordinate axes. c. (iii) Calculate the area of the triangle formed by the tangent and the two coordinate axes.

Browse the problem library