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Given:

lines x + y = 4 and 2x – 3y = 1

To find:

The equation of the straight line drawn through the point of intersection of the lines x + y = 4 and 2x – 3y = 1 and perpendicular to the line cutting off intercepts 5, 6 on the axes.

Explanation:

The equation of the straight line passing through the point of intersection of x + y = 4 and 2x − 3y = 1 is

x + y − 4 + λ(2x − 3y − 1) = 0

⇒ (1 + 2λ)x + (1 − 3λ)y − 4 − λ = 0 … (1)

⇒ y

The equation of the line with intercepts 5 and 6 on the axis is

… (2)

The slope of this line is

The lines (1) and (2) are perpendicular.

∴

⇒ λ

Substituting the values of λ in (1), we get the equation of the required line.

⇒

⇒ 25x – 30y – 23 = 0

Hence, required equation is 25x – 30y – 23 = 0