JEE Main 2022 · 25 Jul · Shift 2 · Mathematics Q29

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MathematicsInteger+4 / -1Question 29 of 90

Let the area enclosed by the $x$ -axis, and the tangent and normal drawn to the curve $4x^3-3xy^2+6x^2-5xy-8y^2+9x+14=0$ at the point $(-2,3)$ be A. Then 8A is equal to ______.

Your answer

Answer and worked solution

Official answer: 170

Slope at $(-2,3)$ : $F_x=-9$ , $F_y=-2$ , so $y'=-\frac92$ .

Intercepts. Tangent at $x=-\frac43$ , normal at $x=-\frac{31}2$ .

Area $\frac12\cdot\frac{85}6\cdot3=\frac{85}4$ ; $8A=170$ .

Answer: 170

Topics:Tangents and normals Chain rule and implicit differentiation

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JEE Main 2022 · 25 Jul · Shift 2, Mathematics question 29