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JEE Main202227 Jul 2022Morning ShiftMathematicsApplication of DerivativesActual

Let M and N be the number of points on the curve y 5 - 9 x y + 2 x = 0 , where the tangents to the curve are parallel to x -axis and y -axis, respectively. Then the value of M + N equals _______.

Correct answer

0

Step-by-step solution

Given, y 5 - 9 x y + 2 x = 0   . . . . . . . 1 Now differentiating both side we get, 5 y 4 d y x - 9 x d y d x - 9 y + 2 = 0 ⇒ d y d x 5 y 4 - 9 x = 9 y - 2 ⇒ d y d x = 9 y - 2 5 y 4 - 9 x = 0   . . . . . 2 ⇒ 9 y - 2 = 0 (for horizontal tangent) ⇒ y = 2 9 , which does not satisfy the original equation so M = 0 . As 2 9 5 - 9 x × 2 9 + 2 x = 0 ⇒ 2 9 5 - 2 x + 2 x = 0 ⇒ 2 9 5 = 0   which is a false statement Now 5 y 4 - 9 x = 0 (from equation

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