Question 386442
The line 3x + 4y = 15 intersects the curve 2xy = 9 at A and B. Find 
a) the coordinates of A and of B, 
b) the distance AB
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3x+4y=15
2xy=9
y= 9/2x
substitute the value of y in first equation
3x+4y=15
3x+4*(9/2x)=15
multiply by 2x
6x^2+36=30x
6x^2-30x+36=0
/6
x^2-5x+6=0
x^2-3x-2x+6=0
x(x-3)-2(x-3)=0
(x-3)(x-2)=0
x=3 OR x=2
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plug value of x in the equation 2xy=9
2*3*y=9
6y=9
y=9/6
y=3/2
(3,3/2)
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2*2*y=9
4y=9
y=9/4
(2,9/4)
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Distance = {{{sqrt((x1-x2)^2+(y1-y2)^2)}}}
Distance ={{{sqrt((3-2)^2+((3/2)-(9/4))^2)}}}
Distance= 1.25
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{{{graph(300,300,-5,5,-5,5,((-3x/4)+(15/4)),(9/2x))}}}