Let PQbe a diameter of the circle x^2+y^2=9. If and 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

Question

Accepted Answer

Correct answer: 7. (7) Let P (3 cos ⁡ ,3 sin ⁡ ) Q (-3 cos ⁡ ,-3 sin ⁡ ) = ( 3 cos +3 sin -2 2 ) = ( -3 cos -3 sin -2 ∣ 2 ) αβ= ∣ (3 cos ⁡ +3 sin ⁡ )^2-42 = ( 5+9 sin2 2 ) αβ |_ max= 5+92=7 (When sin ⁡2 =1)

$Let PQ be a diameter of the circle x^{2} + y^{2} = 9 . If α and β are the lengths of the perpendiculars from P and Q on the straight line, x + y = 2 respectively, then the maximum value of αβ is$

Solution

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