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प्रश्न
If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be ______.
विकल्प
2x + 3y = 12
3x + 2y = 12
4x – 3y = 6
5x – 2y = 10
उत्तर
If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be 2x + 3y = 12.
Explanation:
Let the given line meets the axes at A(a, 0) and B(0, b).
Given that C(3, 2) is the mid-point of AB
∴ 3 = (a + 0)/2`
⇒ a = 6
And 2 = `(0 + b)/2`
⇒ b = 4
Intercept form of the line AB
`x/a + y/b` = 1
⇒ `x/6 + y/4` = 1
⇒ 2x + 3y = 12
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