The line `(x-2)/3=(y+1)/2=(z-1)/1` intersects the curve `x y=c^(I2),z=0` if `c` is equal to

Options

A. ` pm 1 `
B. ` pm ( 1 ) / ( 3 ) `
C. ` pm sqrt 5 `
D. None of these

Answer

C

Explanation

We have, z = 0 for the point where the line intersects the curve
` therefore (x - 2 ) / (3 ) = ( y + 1 ) / ( 2 ) = ( 0 - 1 ) / ( - 1 ) `
` rArr ( x - 2 ) / ( 3 ) = 1 and ( y +1 )/ ( 2 ) = 1 `
` rArr x = 5 and y = 1 `
Put these values in ` xy = c^ 2 ` , we get
` 5 = c ^ 2 rArr c = pm sqrt 5 `