ABSTRACT
Practice Exercise 180 Differentiation of parametric equations (Answers on page 677)
1. Given x=3t−1 and y= t (t−1), determine dy dx
in terms of t
2. A parabola has parametric equations: x= t2, y=2t . Evaluate dy
dx when t=0.5
3. The parametric equations for an ellipse are x=4 cosθ , y = sin θ . Determine (a) dy
dx (b) d
4. Evaluate dy dx
at θ= π 6
radians for the hyperbola whose parametric equations are x=3 sec θ , y=6 tan θ
5. The parametric equations for a rectangular hyperbola are x=2t , y= 2
t . Evaluate
dy dx
when t= 0.40 The equation of a tangent drawn to a curve at point (x1, y1) is given by:
y− y1 = dy1dx1 (x − x1)
Use this in Problems 6 and 7.
