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Let a variable line passing through the centre of the circle x²＋y²- 16x - 4y = 0, meet the positive co-ordinate axes at the point A and B. Then the minimum value of OA + OB, where O is the origin, is equal to
(1) 12
(2) 18
(3) 20
(4) 24

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Answer:Correct option is (2) 18 (y – 2) = m(x – 8)  ⇒ x-intercept ⇒ \(\left(\frac {-2}{m}+8\right)\) ⇒ y-intercept  ⇒ (–8m + 2) ⇒ OA + OB = \(\frac {-2}{m^2}+8 - 8m + 2\) \(f'(m) = \frac {2}{m^2}-8 = 0\) ⇒ m2 = 1/4 ⇒ m = -1/2 ⇒ \(f\left(\frac {-1}{2}\right)= 18\) ⇒ Minimum = 18Read more on Sarthaks.com - https://www.sarthaks.com/3593088/the-line-passes-through-the-centre-of-circle-x-2-y-2-16x-4y-0

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