JEE Main 2022 · 27 Jul · Shift 1 · Mathematics Q26

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MathematicsInteger+4 / -1Question 26 of 90

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

Your answer

Answer and worked solution

Official answer: 2

Slope. $\frac{dy}{dx}=\frac{9y-2}{5y^4-9x}$ .

Horizontal tangents need $y=\frac29$ , but then the curve gives $\left(\frac29\right)^5=0$ . Impossible, so $M=0$ .

Vertical tangents need $5y^4=9x$ . With $x=\frac{y^5}{9y-2}$ this gives $36y^5=10y^4$ : $y=0$ or $y=\frac5{18}$ , so $N=2$ .

Answer: 2

Topics:Tangents and normals Chain rule and implicit differentiation

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JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 26