The line $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1}$ intersects the curve $xy = c^2 , z= 0 $, if c =
Answer & explanation
Correct answer: option 3
At the point on the line where it intersects the given curve, we have z = 0, so that
$\frac{x-2}{3}=\frac{y+1}{2}=\frac{0-1}{-1}$
$⇒ \frac{x-2}{3}=1$ and $ \frac{y+1}{2}=1⇒ x = 5 $ and $y =1.$
Putting these values of x and y in $xy = c^2 $, we get $c^2 = 5 ⇒ c = ±\sqrt{5}$