Q76 / 150 · MHT CET 2026 (19 April Shift 1) · Mathematics
The symmetric form of the equation of the line $x = ay + b$, $z = cy + d$ is
- A$\dfrac{x - a}{b} = y = \dfrac{z - c}{d}$
- B$\dfrac{x - b}{a} = \dfrac{y - d}{c} = z$
- C$x = \dfrac{y - a}{b} = \dfrac{z - c}{d}$
- Correct answerD$\dfrac{x - b}{a} = y = \dfrac{z - d}{c}$
Solution
Given equations of the line are $x = ay + b$ and $z = cy + d$.
From the first equation, expressing $y$ in terms of $x$:
$x - b = ay \Rightarrow y = \dfrac{x - b}{a}$
From the second equation, expressing $y$ in terms of $z$:
$z - d = cy \Rightarrow y = \dfrac{z - d}{c}$
Equating the expressions for $y$, the symmetric form of the line is:
$\dfrac{x - b}{a} = y = \dfrac{z - d}{c}$
Answer: $\dfrac{x - b}{a} = y = \dfrac{z - d}{c}$
From the first equation, expressing $y$ in terms of $x$:
$x - b = ay \Rightarrow y = \dfrac{x - b}{a}$
From the second equation, expressing $y$ in terms of $z$:
$z - d = cy \Rightarrow y = \dfrac{z - d}{c}$
Equating the expressions for $y$, the symmetric form of the line is:
$\dfrac{x - b}{a} = y = \dfrac{z - d}{c}$
Answer: $\dfrac{x - b}{a} = y = \dfrac{z - d}{c}$
Hence, the correct answer is option: 'D'.