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JEE MATHEMATICS MCQ: PARABOLA

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Analyzing +4 | -1
Let P:y2=4ax,a>0P: y^2=4 a x, a>0 be a parabola with focus SS. Let the tangents to the parabola PP make an angle of π4\frac{\pi}{4} with the line y=3x+5y=3 x+5 touch the parabola PP at AA and BB. Then the value of a for which A,BA, B and SS are collinear is
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Correct option: D
any a>0a>0
Option D (any a>0a>0) is correct because the condition for collinearity of A, B, and S holds true regardless of the value of 'a'.

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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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