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JEE MATHEMATICS MCQ: PARABOLA

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P1:y2=49xP_1: y^2=49 x and P2:x2=4ayP_2: x^2=4 a y are two parabolas. Equation of a tangent to the parabola P1P_1 at a point where it intersects the parabola P2P_2 is:
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Correct option: C
x−2y+4a=0x-2 y+4 a=0
Option A (x−2y+4a=0x-2 y+4 a=0) is correct because it represents the tangent to the parabola P1P_1 at the point where it intersects P2P_2, derived from solving the system of equations and finding the tangent.

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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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