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The distance between the points $A$ and $B$ is $\sqrt{34}.$ If $A = (a,4)$ and $B = (-20,33),$ then find the sum of all possible values of $a.$

 Mar 23, 2024
 #1
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This is impossible

 

 (x + 20)^2  + (y - 33)^2  = 34   is a  circle centered at ( -20, 33) with a radius of sqrt (34)

 

Every point on the line  y =  4  is   more than   sqrt (34)  units away from the center of this  circle

 

See the graph below

 

 

cool cool cool

 Mar 23, 2024

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