Question

The line $y=2t^2$ intersects the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ in real points, if

• A. $|t|\le 1$
• B. $|t|<2$
• C. $|t|>1$
• D. $|t|\ge 1$

Answer 1

The correct option is A $|t|\le 1$

For the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ length of semi minor axis(along y-axis) is $2$ so, $-2\le y<2$

$\Rightarrow -2\le 2t^2\le 2-1\le t^2\le 1$

Byt $t^2\le 0$

$\Rightarrow 0\le t^2\le 1\Rightarrow -1\le t\le 1\Rightarrow |t|\le 1\therefore |t|\le 1$