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JEE MATHEMATICS MCQ: PARABOLA

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Application +4 | -1
A common tangent is drawn to the circle x2+y2=c2x^2+y^2=c^2 and the parabola y2=4axy^2=4 a x. If the angle which this tangent makes with the axis of xx is π/4\pi / 4 then the relationship between a and c(a,c>0)c(a, c>0) is-
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Correct option: A
a=2c\mathrm{a}=\sqrt{2} \mathrm{c}
Option D (2x+y−33=02 x+y-3 \sqrt{{3}}=0) is correct because it is the equation of the tangent calculated at the point where the ordinate and abscissa are equal on the curve.

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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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