If a straight line having negative slope passing through the point P = (8, 2) meets the x-axis at A and y-axis at B respectively. Then the minimum value of OA + OB (O being origin) is _____

Question

Smart Achievers · Accepted Answer

(2)

$Equation of line is y - 2 = m (x - 8),$ $O A = 8 + \frac{2}{- m}$ and $O B = 8 (- m) + 2$

$O A + O B = 10 + 8 (- m) + \frac{2}{- m} \geq 18$ $(AM \geq GM)$

Solution

Q.
If a straight line having negative slope passing through the point P = (8, 2) meets the x-axis at A and y-axis at B respectively. Then the minimum value of OA + OB (O being origin) is _____

1 20

2 18

3 10

4 15

Ans.
(2)

$Equation of line is y - 2 = m (x - 8),$ $O A = 8 + \frac{2}{- m}$ and $O B = 8 (- m) + 2$

$O A + O B = 10 + 8 (- m) + \frac{2}{- m} \geq 18$ $(AM \geq GM)$

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