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JEE MATHEMATICS MCQ: PARABOLA

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If y1,  y2{y_1},\;{y_2} and y3{y_3} are the ordinates of the vertices of a triangle inscribed in the parabola y2=4ax{y^2} = 4ax, then its area is
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Correct option: C
18a∣(y1−y2)(y2−y3)(y3−y1)∣\frac{1}{{8a}}\left| {\left( {{y_1} - {y_2}} \right)\left( {{y_2} - {y_3}} \right)\left( {{y_3} - {y_1}} \right)} \right|
Option C (\frac{1}{{8a}}\left| {\left( {{{y_1} - {y_2}} \right)\left( {{{y_2} - {y_3}} \right)\left( {{{y_3} - {y_1}} \right)} \right|\frac{1}{{8a}}\left| {\left( {{{y_1} - {y_2}} \right)\left( {{{y_2} - {y_3}} \right)\left( {{{y_3} - {y_1}} \right)} \right|) is correct because it represents the area of a triangle inscribed in a parabola in terms of the ordinates of the vertices.

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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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