Points (3, 3), (b, 0), (0, k) are collinear and a/b + b/k = 1/3. Then

Question

Points (3, 3), ( $h$ , 0), (0, $k$ ) are collinear and $\frac{a}{h} + \frac{b}{k} = \frac{1}{3}$ . Then

Smart Achievers · Accepted Answer

(3)

$Points (3, 3), (h, 0) and (0, k) are collinear, so one$ $point will lie on the line joining the other two points.$

$i.e. y - 0 = \frac{k - 0}{0 - h} (x - h)$

$∴$ $3 = - \frac{k}{h} (3 - h)$ $(∵ (3, 3) lies on the line)$

$\Rightarrow$ $\frac{3}{h} + \frac{3}{k} = 1 \Rightarrow \frac{1}{h} + \frac{1}{k} = \frac{1}{3}$

$Comparing with$ $\frac{a}{h} + \frac{b}{k} = \frac{1}{3},$ $we get$ $a = 1,$ $b = 1$

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