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JEE Main20204 Sep 2020Evening ShiftMathematicsStraight LinesActual

Let P Q be a diameter of the circle x 2 + y 2 = 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 α β is _______

Correct answer

0

Step-by-step solution

Let P ( 3 cos θ , 3 sin θ ) ∴ Q ( - 3 cos θ , - 3 sin θ ) given line x + y - 2 = 0 ∴ α = | 3 cos θ + 3 sin θ - 2 | 2 β = | - 3 cos θ - 3 sin θ - 2 | 2 ∴    α β = ( 3 cos θ + 3 sin θ - 2 ) · ( 3 cos θ + 3 sin θ + 2 ) 2 = 9 ( 1 + sin 2 θ ) - 4 2 ∴ maximum of α β = 7

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