Equation of Vertical Line
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Then the equation of $\mathcal L$ can be given by:
- $x = a$
- $x \cos \alpha + y \sin \alpha = p$
- $p$ is the length of a perpendicular $\mathcal P$ from $\mathcal L$ to the origin.
- $\alpha$ is the angle made between $\mathcal P$ and the $x$-axis.
Thus $\alpha = 0$ and $p = a$
Hence the equation of $\mathcal L$ becomes:
|\(\displaystyle x \cos 0 + y \sin 0\)||\(=\)||\(\displaystyle a\)|
|\(\displaystyle \leadsto \ \ \)||\(\displaystyle x\)||\(=\)||\(\displaystyle a\)||Sine of Zero is Zero, Cosine of Zero is One|
Hence the result.