JEE Main 2021 · 24 Feb · Shift 1 · Mathematics Q75

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MathematicsSingle correct+4 / -1Question 75 of 90

If the tangent to the curve $y=x^3$ at the point P(t, t $^3$ ) meets the curve again at Q, then the ordinate of the point which divides PQ internally in the ratio 1 : 2 is :

2t^3

-t^3

-2t^3

Answer and worked solution

Official answer: D

Second intersection. $x^3-3t^2x+2t^3=(x-t)^2(x+2t)$ , so $Q=(-2t,-8t^3)$ .

Dividing point $\frac{2P+Q}3$ has ordinate $\frac{2t^3-8t^3}3=-2t^3$ .

(D)

Topics:Tangents and normals Distance and section formulae

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JEE Main 2021 · 24 Feb · Shift 1, Mathematics question 75