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JEE Main202126 Feb 2021Evening ShiftMathematicsApplication of DerivativesActual

Let the normals at all the points on a given curve pass through a fixed point a , b . If the curve passes through 3 , - 3 and 4 , - 2 2 , given that a - 2 2 b = 3 , then a 2 + b 2 + a b is equal to _____.

Correct answer

0

Step-by-step solution

All normals of circle passes through centre Radius = C A = C B C A 2 = C B 2 a - 3 2 + b + 3 2 = a - 4 2 + b + 2 2 2 a + 3 - 2 2 b = 3 a - 2 2 b + 3 b = 3       . . . 1 given that a - 2 2 b = 3         . . . 2 from 1 and 2 ⇒ a = 3 , b = 0 a 2 + b 2 + a b = 9

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