Question

If points A(h, 0), B(0, k) and C(a, b) lie on a line then show that `"a"/"h" + "b"/"k"` = 1

Answer 1

A(h, 0), B(0, k) and C(a, b) lie on a line.

∴ A, B, C are collinear.

∴ slope of AB = slope of BC

∴ `("k" - 0)/(0 - "h") = ("b" - "k")/("a" - 0)`

∴ `- "k"/"h" = ("b" - "k")/"a"`

∴ – ak = bh – hk

∴ ak + bh = hk

∴ `("ak" + "bh")/"hk"` = 1

∴ `"a"/"h" + "b"/"k"` = 1

which is the required condition.