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JEE MATHEMATICS MCQ: PARABOLA

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Analyzing +4 | -1
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
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Correct option: C
(−2,0)\left( { - 2,0} \right)
Option C ((−2,0)\left( { - 2,0} \right)) is correct because it is the vertex of the parabola that represents the locus of the midpoint of the chord PR.

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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 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 The equation of the parabola with its vertex at the origin, axis on the y−axisy - axis and passing through the point (6,−3)\left( {6, - 3} \right) is
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