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Given that x+y=13 and xy=24, find the distance from the point (x,y) to the origin. 

 Jul 12, 2022
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x + y =  13    square both sides   x^2 + 2xy + y^2  = 169      (1)

xy = 24   →   2xy  =  48     (2)

 

Sub  (2)  into (1)

 

x^2 + 48 + y^2 = 169

 

x^2 + y^2 =  121

 

x^2 + y^2  = 11^2

 

The smallest distance is 11 units

 

See the graph here :  https://www.desmos.com/calculator/6q6v3gi6wa

 

 

cool cool cool

 Jul 13, 2022

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