Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaChordsMedium2 minPYQ_2015
MathematicsMediummultiple choice

LetPandQbe distinct points on the parabolay2=2x such that a circle withPQas diameter passes through the vertexOof the parabola. IfPlies in the first quadrant and the area of the triangleΔOPQis32, then which of the following is (are) the coordinates ofP?

Options:(select one or more)

Answer:
A, D
Solution:

=32

1200t122t1t222t200

12t12t22-t22t12=±32

14t1t2t1-t2=±32

t1t2t1-t2=±122

t1-t2=±32

  t1-t2=32 (as t1>t2)

t1+t2=18-16=±2

2t1=32+2

t1=22

2t1=22

t1=2

P4,22 and P1,2

Stream:JEE_ADVSubject:MathematicsTopic:ParabolaSubtopic:Chords
2mℹ️ Source: PYQ_2015

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