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JEE Main20209 Jan 2020Evening ShiftMathematicsApplication of DerivativesActual

If the curves, x 2 - 6 x + y 2 + 8 = 0 and x 2 - 8 y + y 2 + 16 - k = 0 , k > 0 touch each other at a point, then the largest value of k is ____________.

Correct answer

0

Step-by-step solution

If general equation of circle is x 2 + y 2 + 2 g x + 2 f y + c = 0 then its center is - g , - f and radius is g 2 + f 2 - c Two circles touches each other if C 1 C 2 = r 1 ± r 2 Distance between C 2 3 , 0 a n d C 1 0 , 4 is either k + 1 o r k - 1 C 1 C 2 = 3 - 0 2 + 0 - 4 2 = 5 ⇒ k + 1 = 5 or k + 1 = 5 ⇒ k = 16 or k = 36 ⇒ Maximum value of k is 36 .

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