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For the curve $x=t^2-1, y=t^2-t$, the tangent line is perpendicular to x - axis when |
$t=0$ $t=\infty$ $t=1 / \sqrt{3}$ $t=-1 / \sqrt{3}$ |
$t=0$ |
We have, $x=t^2-1, y=t^2-t$ ∴ $\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{2 t-1}{2 t}$ If the tangent is perpendicular to x - axis, then $\frac{d x}{d y}=0 \Rightarrow \frac{2 t}{2 t-1}=0 \Rightarrow t=0$ |
