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Line AB passes through point (2,3) and intersects the positive x and y-axes at A(a,0) and B(0,b), respectively. If the area of ΔAOB is 11, then the value of 4b2+9a2 is_____

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answer is 220.

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Detailed Solution

Area of ΔAOB,ab2=11∴ ab=22But points Aa,0,B0,b  and P2,3 are collinear.⇒−ba=3−02−a⇒−2b+ab=3a⇒3a+2b=22Squaring 9a2+4b2+12ab=484⇒9a2+4b2=220
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