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JEE MATHEMATICS MCQ: PARABOLA

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From a point (sin⁡θ,cos⁡θ)(\sin \theta, \cos \theta), if three normals can be drawn to the parabola y2=4axy^2=4 a x, then the value of aa is
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Correct option: D
(−12,0)∪(0,12)\left(\frac{-1}{2}, 0\right) \cup\left(0, \frac{1}{2}\right)
Option D ((−12,0\frac{{-1}}{{2}}, 0) ∪\cup (0,120, \frac{{1}}{{2}})) is correct because it defines the range of 'a' for which three normals can be drawn from the given point to the 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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