Let a variable line of slope m 0 passing through the point ( 4 , − 9 ) intersect the coordinate axes at the points A and B . The minimum value of the sum of the distances of A and B from the origin

Question

Let a variable line of slope m > 0 passing through the point ( 4 , − 9 ) intersect the coordinate axes at the points A and B . The minimum value of the sum of the distances of A and B from the origin is

TestHub · Accepted Answer

equation of line is ​ y + 9 = m ( x − 4 ) ∴ A = ( m 9 + 4 m ​ , 0 ) B = ( 0 , − 9 − 4 m ) ∴ O A + OB = m 9 + 4 m ​ + 9 + 4 m ​ ​ ∵ m > 0 = 13 + m 9 ​ + 4 m ∵ 2 4 m + m 9 ​ ​ ≥ 36 ​ ⇒ 4 m + m 9 ​ ≥ 12 ∴ OA + OB ≥ 25 ​

Mathematics - Straight Lines Question with Solution | TestHub

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