Mathematics - Parabola Question with Solution | TestHub
MathematicsParabolaChordsMedium2 minQB
MathematicsMediuminteger
Passage / Comprehension
Let PQ be a focal chord of the parabola y² = 8x with focus F, where P lies in the first quadrant and PF = 6. O is the origin.
The square of the area of triangle OPQ equals ______ .
Answer:
72
Solution:
The focal chord PQ of y² = 8x passes through F(2, 0). PF = x + 2 = 6 gives x = 4 for P, so P = (4, 4√2). The other end is Q = (1, -2√2) (parameters t1 = √2 and t2 = -1/√2 satisfy t1t2 = -1). With O = (0, 0), the area = (1/2)|4(-2√2) - 1(4√2)| = (1/2)(12√2) = 6√2. So (area)² = 72.
Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Chords
⏱ 2mℹ️ Source: QB
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