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Find the y-intercept of the graph x^2 - 10x + y^2 - 10y + 25 = 8x + 4y + 16. Write your answer as an ordered pair.

 Feb 10, 2021
 #1
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The y axis intercept occurs when x = 0    so put x = 0 into the equation and solve for y value

 

y^2 -10y + 25 = 4y + 16

y^2 -14y +9 = 0

   If you use the quadratic formula to find y = two roots   so the equation of the circle intersects the y -axis at two points....

  y=  7 +- 2 sqrt (10)      and x = 0 for each of the points

 Feb 10, 2021
 #2
avatar+120129 
+1

Not as tough as it seems

 

x^2 - 10x + y^2 - 10y + 25 = 8x + 4y + 16      simplify as

 

x^2  -10x - 8x + y^2 - 10y  -4y   + 25  - 16   =    0

 

x^2  - 18x  + y^2 - 14y  +  9  = 0

 

x^2  -18x  +  y^2  -14y    =  -9       complete the square on  x and  y

 

x^2  -18x  + 81  +  y^2 - 14y + 49  =   -9 + 81 + 49

 

(x - 9)^2   + ( y - 7)^2   = 121

 

To find the y intercept, let  x   = 0

 

(0 - 9)^2  + ( y -7)^2  = 121

 

81 +  ( y -7)^2   = 121

 

(y -7)^2   =   121  -81

 

(y - 7)^2   =40      take both roots

 

y - 7  = ± sqrt (40)   =  ± 2sqrt (10)

 

So ....two y intercepts

 

y = (0,  7  - 2sqrt (10)  )

 

And 

 

y =  (0, 7 + 2sqrt (10)  )

 

 

cool cool cool

 Feb 10, 2021

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