For the curve $x=t^2-1, y=t^2-t$, the tangent line is perpendicular to x - axis when
Answer & explanation
Correct answer: option 1
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
$\frac{d x}{d y}=0 \Rightarrow \frac{2 t}{2 t-1}=0 \Rightarrow t=0$