1. Tardigrade
  2. Question
  3. Mathematics
  4. C is a curve defined by the parametric equation x=t2 and y=t3-3 t. The equation of the tangent line to this curve at (4,2) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. $C$ is a curve defined by the parametric equation $x=t^2$ and $y=t^3-3 t$. The equation of the tangent line to this curve at $(4,2)$ is

Application of Derivatives

Solution:

Slope $M =\frac{ dy }{ dx }=\frac{ dy / dt }{ dx / dt }$
$M =\frac{3 t ^2-3}{2 t } \text { at } t =2$
$M =\frac{9}{4} $
Equation of tangent at $(4,2) \cdot M=\frac{9}{4}$
$(y-2)=\frac{9}{4}(x-4) \Rightarrow y=\frac{9}{4} x-7$