Let P(3cosθ,3sinθ)∴Q(−3cosθ,−3sinθ)
given line x+y−2=0 ∴α=2∣3cosθ+3sinθ−2∣
β=2∣−3cosθ−3sinθ−2∣
∴αβ=∣2(3cosθ+3sinθ−2)⋅(3cosθ+3sinθ+2)∣=∣29(1+sin2θ)−4∣
∴ maximum of αβ=7
Let PQ be a diameter of the circle x2+y2=9. If α and β are the lengths of the perpendiculars from P and Q on the straight line, x+y=2 respectively, then the maximum value of αβ is _______
Held on 4 Sept 2020 · Verified 6 Jul 2026.
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