If the length of perpendicular drawn from the point $(4,1)$ on the line $3 x-4 y+k=0$ is 2 units, then the…
If the length of perpendicular drawn from the point $(4,1)$ on the line $3 x-4 y+k=0$
is 2 units, then the values of $\mathrm{k}$ are
- $2,-18$
- $-2,-18$
- $-2,1$
- $-2,18$
Solution
We have, point $(4,1)$ and $3 x-4 y+k=0$
$\begin{array}{l}
\therefore\left|\frac{3 \times 4-4 \times 1+k}{\sqrt{9+16}}\right|=2 \Rightarrow\left|\frac{12-4+k}{\sqrt{25}}\right|=2 \\
8+k \mid=10 \Rightarrow \pm(8+k)=10 \\
8+k=10 \text { or }-8-k=10 \Rightarrow k=2 \text { or } k=-18
\end{array}$
Asked in: MHT CET 2020 (19 Oct Shift 1)
Practice more Straight Lines questions on Aicharya