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JEE MATHEMATICS MCQ: PARABOLA

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If P(t1),Q(t2)P\left(t_1\right), Q\left(t_2\right) and R(t3)R\left(t_3\right) are three points on the parabola y2=4axy^2=4 a x, then area of ΔPQR=\Delta P Q R=
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Correct option: B
a2∣(t1−t2)(t2−t3)(t3−t1)∣a^2\left|\left(t_1-t_2\right)\left(t_2-t_3\right)\left(t_3-t_1\right)\right|
Option A (a∣(t1−t2)(t2−t3)(t3−t1)∣a|(t_1-t_2)(t_2-t_3)(t_3-t_1)|) is correct because it represents the area of the triangle formed by three points on the parabola in terms of their parameters.

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The equation of a common tangent to the parabolas y=x2y=x^2 and y=−(x−2)2y=-(x-2)^2 is A point PP moves such that slope of one tangent drawn from it to parabola y2=16xy^2=16 x is four times the slope of other tangent, then the length of latus rectum of the conic represented by locus of PP, is Let P,Q,RP,Q,R be three points on parabola y2=4x{y^2} = 4x and normal at PP and RR meet at QQ, then the locus of the mid-point of the chord PRPR is a parabola whose vertex is at The tangents at the end points of any chord through (1,0)(1,0) to the parabola y2+4x=8y^2+4 x=8 intersect The focus of the parabola x2=−16yx^2=-16 y is If II denotes the semi-latusrectum of the parabola y2=4ax{y^2} = 4ax and SPSP and SQSQ denote the segments of any focal chord PQ,SPQ,S being the focus, then SP,lSP,l and SQSQ are in the relation
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