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Question
Find the equation of a line drawn perpendicular to the line \[\frac{x}{4} + \frac{y}{6} = 1\] through the point where it meets the y-axis.
Solution
Let us find the intersection of the line \[\frac{x}{4} + \frac{y}{6} = 1\] with y-axis.
At x = 0,
\[0 + \frac{y}{6} = 1\]
\[ \Rightarrow y = 6\]
Thus, the given line intersects y-axis at (0, 6).
The line perpendicular to the line \[\frac{x}{4} + \frac{y}{6} = 1\] is \[\frac{x}{6} - \frac{y}{4} + \lambda = 0\]
This line passes through (0, 6).
\[0 - \frac{6}{4} + \lambda = 0\]
\[ \Rightarrow \lambda = \frac{3}{2}\]
Now, substituting the value of \[\lambda\],we get:
\[\frac{x}{6} - \frac{y}{4} + \frac{3}{2} = 0\]
\[ \Rightarrow 2x - 3y + 18 = 0\]
This is the equation of the required line.
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