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JEE MATHEMATICS MCQ: PARABOLA

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The vertex of a parabola is the point (a,b)(a, b) and Latusrectum is of length l.l. If the axis of the parabola is along the positive direction of yy-axis, then its equation is
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Correct option: B
(xāˆ’a)2=l2(2yāˆ’2b)(x-a)^2=\frac{l}{2}(2 y-2 b)
Option B ((xāˆ’a)2=l2(2yāˆ’2b)(x-a)^2=\frac{l}{2}(2 y-2 b)) is correct because it represents a parabola with vertex (a,b), latus rectum l, and axis along the positive y-axis.

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