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Question
Answer the following question:
Find the equation of the line which contains the point A(3, 5) and makes equal intercepts on the co-ordinates axes.
Solution
Case I: Line not passing through the origin.
Let the equation of the line be `x/"a" + y/"b"` = 1 ...(i)
This line passes through A(3, 5).
∴ `3/"a" + 5/"b"` = 1 ...(ii)
Since the required line makes equal intercepts on the co-ordinates axes,
a = b ...(iii)
Substituting the value of b in (ii), we get
`3/"a" + 5/"a"` = 1
∴ `8/"a"` = 1
∴ a = 8
∴ b = 8 …[From (iii)]
Substituting the values of a and b in equation (i), the equation of the required line is
`x/8 + y/8` = 1
∴ x + y = 8
Case II: Line passing through the origin.
Slope of line passing through origin and
A(3, 5) is m = `(5 - 0)/(3 - 0) = 5/3`
∴ Equation of the line having slope m and passing through the origin (0, 0) is y = mx.
∴ The equation of the required line is
y = `5/3x`
∴ 5x – 3y = 0
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