Practicing Success
The slope of the tangent to the curve $x=t^2+3 t-8, y=2 t^2-2 t-5$ at the point (2, -1), is |
$\frac{22}{7}$ $\frac{6}{7}$ -6 none of these |
$\frac{6}{7}$ |
For the point (2, -1) on the curve $x=t^2+3 t-8, y=2 t^2-2 t-5$, we have $t^2+3 t-8=2$ and $ 2 t^2-2 t-5=-1$ $\Rightarrow t^2+3 t-10=0$ and $ 2 t^2-2 t-4=0$ $\Rightarrow (t+5)(t-2)=0$ and $(t-2)(t+1)=0$ $\Rightarrow t=2$ Now, $\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{4 t-2}{2 t+3} \Rightarrow\left(\frac{d y}{d x}\right)_{t=2}=\frac{4 \times 2-2}{2 \times 2+3}=\frac{6}{7}$ |