An ellipse centred at the origin is represented parametrically by and .

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

An ellipse centred at the origin is represented parametrically by

x=4\cos t

and

y=3\sin t

. (i) Derive the equation of the tangent to the ellipse at the general parameter value

t

. (ii) For

t=\dfrac{\pi}{6}

, obtain the intercept form of the tangent, i.e.

\dfrac{x}{p}+\dfrac{y}{q}=1

, and determine the intercepts

p

and

q

made on the coordinate axes. (iii) Calculate the area of the triangle formed by this tangent with the coordinate axes.