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JEE MATHEMATICS MCQ: PARABOLA

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Application +4 | -1
If f(x+y)=f(x)⋅f(y)f(x+y)=f(x) \cdot f(y) for all x,y∈Rx, y \in R and f(1)=2f(1)=2 and ar=f(r)a_r=f(r), for r∈Nr \in N then the coordinates of a point on the parabola y2=8xy^2=8 x whose focal distance is 4 may be
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Correct option: A
(a1,a2)\left(a_1, a_2\right)
Option A ((a1,a2)\left(a_1, a_2\right)) is correct because the point (2,4) lies on the parabola and corresponds to the values of a1a_1 and a2a_2 derived from the given function.

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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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