JEE Main 2016 · 9 Apr · Shift 1 · Mathematics Q72

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MathematicsSingle correct+4 / -1Question 72 of 90

If the tangent at a point P, with parameter t, on the curve $x=4t^2+3$ , $y=8t^3-1$ , $t\in\mathbb R$ , meets the curve again at a point Q, then the coordinates of Q are :

(t^2+3,\ -t^3-1)

(4t^2+3,\ -8t^3-1)

(t^2+3,\ t^3-1)

(16t^2+3,\ -64t^3-1)

Answer and worked solution

Official answer: A

The slope is $\frac{24t^2}{8t}=3t$ . A second point with parameter s on the tangent satisfies $2s^2-ts-t^2=0$ , so $s=-\frac t2$ : Q is $(t^2+3,\,-t^3-1)$ .

Topics:Tangents and normals Parametric differentiation

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JEE Main 2016 · 9 Apr · Shift 1, Mathematics question 72