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Question
Answer the following question:
P(a, b) is the mid point of a line segment between axes. Show that the equation of the line is `x/"a" + y/"b"` = 2
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Solution
Let the intercepts of a line AB be x1 and y1 on the X and Y-axes respectively.
∴ A ≡ (x1, 0), B ≡ (0, y1)
P(a, b) is the midpoint of a line segment AB intercepted between the axes.
∴ P = `(("x"_1+0)/2,(0+"y"_1)/2)`
∴ (a, b) = `("x"_1/2,"y"_1/2)`
∴ a = `"x"_1/2`
∴ x1 = 2a
and b = `"y"_1/2`
∴ y1 = 2b
∴ Equation of the required line AB is
`"x"/"x"_1+"y"/"y"_1` = 1
∴ `"x"/(2"a")+"y"/(2"b")` = 1
∴ `"x"/"a" + "y"/"b"` = 2
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