Answer in Brief

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.

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#### 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.

Concept: Straight Lines - Equation of Family of Lines Passing Through the Point of Intersection of Two Lines

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