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avatar+39 

Let x and y be real numbers. If x and y satisfy: 

 

x^2 + y^2 = 4x  - 8y + 25

then find the largest value of x and simpify giving your answer in exact form and radicals!

 Apr 7, 2024
 #1
avatar+128794 
+1

Simplify as

 

x^2 - 4x  + y^2 + 8y =  25             complete the square on x, y

 

x^2 - 4x +4  +  y^2 + 8y + 16 =  25 + 4 + 16

 

(x - 2)^2  + ( y + 4)^2  =  45

 

This is a  circle  centered at  ( 2 , -4)   with a radius of sqrt (45)  = 3sqrt (5)

 

Largest value of x =   2 + 3sqrt (5)

 

cool cool cool

 Apr 7, 2024
 #2
avatar+39 
+1

thank you so much!

rerebas  Apr 7, 2024

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