The coordinates of a point on the line $x+y+1=0$ which is at a distance $\frac{1}{5}$ unit from the line $3 x+4 y+2=0$ are

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The coordinates of a point on the line $x+y+1=0$ which is at a distance $\frac{1}{5}$ unit from the line $3 x+4 y+2=0$ are

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deepak01 · Answer 1 · 2021-12-20T11:40:34+0000

Ans : (B, D)
Let $(t,-t-1)$ be a parametric point of the line $x+y+1=0$
Distance of $(t,-t-1)$ from $3 x+4 y+2=0$ is
$$
\begin{aligned}
&\frac{|3 t+4(-t-1)+2|}{\sqrt{3^{2}+4^{2}}}=\frac{1}{5} \\
&\Rightarrow|-t-2|=1 \Rightarrow|t+2|=1 \text {, so } t=-1 \text { or } t=-3
\end{aligned}
$$
possible co-ordinates are $(-1,0) \&(-3,2)$

The coordinates of a point on the line \(x+y+1=0\) which is at a distance \(\frac{1}{5}\) unit from the line \(3 x+4 y+2=0\) are

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