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प्रश्न
Find equations of lines containing the point A(3, 4) and making equal intercepts on the co-ordinates axes.
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उत्तर
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, 4).
∴ `3/"a" + 4/"b"` = 1 ...(ii)
Since, the required line make equal intercepts on the co-ordinate axes.
∴ a = b ...(iii)
Substituting the value of b in (ii), we get
`3/"a" + 4/"a"` = 1
∴ `7/"a"` = 1
∴ a = 7
∴ b = 7 ...[From (iii)]
Substituting the values of a and b in (i), equation of the required line is
`x/7 + y/7` = 1
∴ x + y = 7
Case II: Line passing through origin.
Slope of line passing through origin and A(3, 4) is
m = `(4 - 0)/(3 - 0) = 4/3`
∴ Equation of the line having slope m and passing through origin (0, 0) is y = mx.
∴ The equation of the required line is y = `4/3x`
∴ 4x – 3y = 0
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