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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 $4 b^{2} + 9 a^{2}$ is_____

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Detailed Solution

Area of $ΔAOB, \frac{ab}{2} = 11$

$∴ ab = 22$

But points $A (a, 0), B (0, b) and P (2, 3)$ are collinear.

$\Rightarrow - \frac{b}{a} = \frac{3 - 0}{2 - a}$

$\Rightarrow - 2 b + ab = 3 a$

$\Rightarrow 3 a + 2 b = 22$

Squaring $9 a^{2} + 4 b^{2} + 12 ab = 484$

$\Rightarrow 9 a^{2} + 4 b^{2} = 220$

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