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 length PQ equals ______ .
Answer:
9
Solution:
For y² = 8x, a = 2 and F = (2, 0). PF = x_P + 2 = 6 gives x_P = 4, so P = (4, 4√2), i.e. t = √2 for P = (2t², 4t). The other end of a focal chord has parameter -1/t, so Q = (1, -2√2) and FQ = 1 + 2 = 3. Hence PQ = PF + FQ = 6 + 3 = 9.
Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Chords
⏱ 2mℹ️ Source: QB
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