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JEE MATHEMATICS MCQ: PARABOLA

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Analyzing +4 | -1
Let PQP Q be a focal chord of the parabola y2=4axy^2=4 ax such that tangents at PP and QQ meet at a point on the line y=2x+a,a>0y=2 x+a, a>0. If PQP Q subtends an angle θ\theta at the vertex of y2=4axy^2=4 a x, then tan⁑θ=\tan \theta=
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Correct option: D
βˆ’253-\frac{2 \sqrt{5}}{3}
Option D (βˆ’253\frac{-2 \sqrt{5}}{3}) is correct because the tangent of the angle subtended by the focal chord PQ at the vertex is calculated considering the obtuse angle.

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The equation of a common tangent to the parabolas y=x2y=x^2 and y=βˆ’(xβˆ’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=βˆ’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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