The length of the perpendicular from the point $P(a, b)$ to the line $\frac{x}{a}+\frac{y}{b}=1$ is

The length of the perpendicular from the point $P(a, b)$ to the line $\frac{x}{a}+\frac{y}{b}=1$ is
  1. $\mid \frac{\sqrt{a^{2}+b^{2}}}{a b}$ units
  2. $\left|\frac{a b}{\sqrt{a^{2}+b^{2}}}\right|$ units
  3. $\left|\frac{b^{2}}{\sqrt{a^{2}+b^{2}}}\right|$ units
  4. $\left|\frac{a^{2}}{\sqrt{a^{2}+b^{2}}}\right|$ units

Solution

We have line $b x+a y-a b=0$ Length of $\perp e r$ from $P(a, b)$ on the given line is $\left|\frac{b a+a b-a b}{\sqrt{b^{2}+a^{2}}}\right|=\left|\frac{a b}{\sqrt{a^{2}+b^{2}}}\right|$

Asked in: MHT CET 2020 (14 Oct Shift 1)

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