If the equation of a line is $x = ay + b, z = cy + d$, then find the direction ratios of the line and a point on the line.

Direction Ratios: $(a, 1, c)$; Point: $(b, 0, d)$

The correct answer is Option (1) → Direction Ratios: $(a, 1, c)$; Point: $(b, 0, d)$ ##

$x = ay + b ⇒\frac{x - b}{a} = y$

$z = cy + d ⇒\frac{z - d}{c} = y$

$∴$ Equation of the line:

$\frac{x - b}{a} = \frac{y - 0}{1} = \frac{z - d}{c}$

$\textbf{Direction ratios of the line}: (a, 1, c)$

$\textbf{Point on the line}:(b, 0, d)$