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JEE MATHEMATICS MCQ: PARABOLA

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Analyzing +4 | -1
Let the line lx+my=1lx+m y=1 cut the parabola y2=4axy^2=4 a x in the points AA and BB. Normals at AA and BB meet at point CC. Normal from CC other than these two meet the parabola at DD, then the coordinate of DD are
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Correct option: D
(4am2l2,4aml)\left(\frac{4 a m^2}{l^2}, \frac{4 a m}{l}\right)
Option B (3−223-2 \sqrt{2}) is correct because it represents the minimum squared distance between the circle and the parabola, calculated using the common normal.

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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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