If the point $(1, 1)$ lies on the line passing through the points $(a, 0)$ and $(0, b)$ , then : $\frac{1}{a} + \frac{1}{b} =$

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\frac{1}{a b}

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Solution

The correct option is C $1$
Equation of line from point $(a, 0)$ and $(0, b)$
$y = \frac{- b}{a} (x - a)$
$a y = - b x + a b$
$b x + a y = a b$ -----(1)
Point $(1, 1)$ lies on line (1)
$b + a = a b$
$\frac{1}{a} + \frac{1}{b} = 1$

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