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Let \((x,y)\) be an ordered pair of real numbers that satisfies the equation \(x^2+y^2=14x+48y\). What is the maximum value of y?

 Jul 16, 2019
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x^2 + y^2  = 14x + 48y         rearrange as

 

x^2 - 14x  + y^2 - 48y  = 0      complete the square on x and y

 

x^2 -14x + 49 + y^2 - 48y + 576  =  49 + 576        factor  and simplify

 

(x -7)^2  + ( y - 24)^2  =  625

 

This is a circle centered at  ( 7 , 24)   with  a radius of √625  =  25

 

The max value for y will therefore be   24 + 25   =  49

 

 

cool cool cool

 Jul 16, 2019

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