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JEE MATHEMATICS MCQ: PARABOLA

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The circle x2+y2−2x−6y+2=0x^2+y^2-2 x-6 y+2=0 intersects the parabola y2=8xy^2=8 x orthogonally at the point PP. The equation of the tangent to the parabola at PP can be
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Correct option: D
2x−y+1=02 x-y+1=0
Option D (2x−y+1=02x - y + 1 = 0) is correct because it represents a tangent to the parabola that passes through the center of the circle, ensuring orthogonality.

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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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