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The line 2x + 3y = 12 touches the ellipse\frac{x^{2}}{9}+\frac{y^{2}}{4}=2 at the point (3, 2).

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True 

Given line is 2x+3y=12

and the ellipse 4x2+9y2=72

Solving line and ellipse we get (12-3y)2+9y2=72

(4-y)2+y2=8

2y2-8y+8=0

y2-4y+4=0

(y-2)2=0

y=2;x=3

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