Question

The line $x=t$ meets the ellipse $x^2+\frac{y^2}{9}=1$ in real and distinct points if and only if:

• A. $|t|<2$
• B. $|t|<1$
• C. $|t|>1$
• D. None of these

Answer 1

The correct option is B $|t|<1$

Solving the given line and the ellipse, we get
$t^2+\frac{y^2}{9}=1$
$\Rightarrow y^2=9(1-t^2)$,
Which gives real and distinct values of $y$, if $1-t^2>0$
$\Rightarrow t\in (-1,1)$