Question

The line $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1}$ intersects the curve $xy=c^2,z=0$ if c is equal to

• A. $\pm 1$
• B. $\pm \frac{1}{3}$
• C. $\pm \sqrt{5}$
• D. $0$

Answer 1

The correct option is C $\pm \sqrt{5}$

we have, z = 0 for the point where the line intersects the curve
$\therefore \frac{x-2}{3}=\frac{y+1}{2}=\frac{0-1}{-1}\Rightarrow \frac{x-2}{3}=1and\frac{y+1}{2}=1\Rightarrow x=5andy=1$
Put these values in $xy=c^2$
We get, $5=c^2$
$\Rightarrow c=\pm \sqrt{5}$