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JEE MATHEMATICS MCQ: PARABOLA

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Analyzing +4 | -1
In a parabola y2=4ax,y^2 = 4ax, two points PP and QQ are taken such that the tangents drawn to parabola at these points
meet at directrix in R.R. Focus of locus of circumcentre of ΔPQR\Delta PQR will be:
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Correct option: C
(3a2,0)\left( {\frac{{3a}}{2},0} \right)
Option C (3a2,0)\left( \frac{{3a}}{{2}},0 \right) is correct because the locus of the circumcentre is a parabola with focus at (3a2,0)\left( \frac{{3a}}{{2}},0 \right).

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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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