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. None of these.

Answer 1

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

we have $z=0$ for the point where the line intersects the curve

$\therefore \frac{x-2}{3}=\frac{y+1}{2}=\frac{0-1}{-1}$

$⟹\frac{x-2}{3}=1$ and $\frac{y+1}{2}=1$

$\therefore x=5,y=1$

put these values in $xy=c^2$

we get $c^2=5$

$=\pm \sqrt{5}$