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JEE MATHEMATICS MCQ: PARABOLA

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Let AA be the vertex and LL the length of the latus rectum of the parabola y2−2y−4x−7=0y^2-2 y-4 x-7=0. The equation of a parabola with AA as vertex, 2 L2 \mathrm{~L} the length of the latus rectum and the axis at right angles to that of the given curve is -
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Correct option: A
x2+4x+8y−4=0x^2+4 x+8 y-4=0
Option A (x2+4x+8y−4=0x^2+4 x+8 y-4=0) is correct because it represents a parabola with the given vertex, latus rectum length, and axis perpendicular to the original parabola.

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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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