JEE Main 2022 · 28 Jun · Shift 1 · Mathematics Q26

← JEE Main 2022 · 28 Jun · Shift 1

MathematicsInteger+4 / -1Question 26 of 90

Let $l$ be a line which is normal to the curve $y=2x^2+x+2$ at a point P on the curve. If the point $Q(6,4)$ lies on the line $l$ and O is origin, then the area of the triangle OPQ is equal to ______.

Your answer

Answer and worked solution

Official answer: 13

Normal at $P(t,2t^2+t+2)$ through $(6,4)$ . $(2-t-2t^2)(4t+1)+6-t=0$ , i.e. $4t^3+3t^2-3t-4=0=(t-1)(4t^2+7t+4)$ .

So $P=(1,5)$ .

Area. $\frac12|1\cdot4-5\cdot6|=13$ .

Answer: 13

Topics:Tangents and normals Distance and section formulae

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JEE Main 2022 · 28 Jun · Shift 1, Mathematics question 26