If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that.

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Solution

It is known that the equation of a line whose intercepts on the axes are a and b is

The perpendicular distance (d) of a line Ax + By + C = 0 from a point (x₁, y₁) is given by.

On comparing equation (1) to the general equation of line Ax + By + C = 0, we obtain A = b, B = a, and C = –ab.

Therefore, if p is the length of the perpendicular from point (x₁, y₁) = (0, 0) to line (1), we obtain

On squaring both sides, we obtain

Hence, we showed that.

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