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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 minimum value of x?

 Feb 11, 2019
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This is an equation of a circle.....

do some re-arranging and completing of the square for x and y to get

 

(x-7)^2 + (y-24)^2 = 25^2        center at    7, 24

 

minimum value of x  will be at    the value of the center point  x   minus the radius      (7 - 25) = - 18

 Feb 11, 2019
edited by ElectricPavlov  Feb 11, 2019

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