NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

If y = m x + 5 is a tangent to x 3 y 3 = a x 3 + b y 3 at point 1,2 , then the value of a is equal to

Options

A9 5
B16 5
C9 4
D18 7

Correct answer

B. 16 5

Step-by-step solution

P 1,2 lies on the curve and line, hence L → 2 = m + 5 ⇒ m = - 3 C u r v e → 8 = a + 8 b Also, d y d x at P 1,2 for the curve should be m = - 3 , i.e. 3 x 2 y 3 + x 3 . 3 y 2 y ' = 3 a x 2 + 3 b y 2 y ' ⇒ 24 + 12 - 3 = 3 a + 12 b - 3 ⇒ - 12 = 3 a - 36 b ⇒ a - 12 b = - 4 & a + 8 b = 8 - 20 b = - 1 2 ⇒ b = 3 5 and a = 16 5

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