The lines which intersect the skew lines `y=m x ,z=c ; y=-m x ,z=-c` and the x-axis lie on the surface a. `c z=m x y` b. `x y=c m z` c. `c y=m x z` d. none of these

Options

A. `cz=mxy`
B. `xy=cmz`
C. `cy=mxz`
D. none of these

Answer

c

Explanation

Equations of the planes through `y=mx,z=candy=-mx,z=-c` are respectively,
`(y-mx)+lamda_(1)(z-c)=0" "(i)`
and `(y+mx)+lamda_(2)(z+c)=0" "(ii)`
It meets at x-axis, i.e., y=0=z.
`becauselamda_(2)=lamda_(1)`
From (i) and (ii), `(y-mx)/(z-c)=(y+mx)/(z+c)`
`becausecy=mzx`