SOLUTION: Solve the system and graph the curves (x+1)^2+2(y-4)^2=12 and y^2-8y=4x-16

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Question 1088213: Solve the system and graph the curves (x+1)^2+2(y-4)^2=12 and y^2-8y=4x-16
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.
(1)    %28x%2B1%29%5E2%2B2%28y-4%29%5E2 = 12 
(2)    y%5E2-8y = 4x-16


(1)    x%5E2+%2B+2x+%2B+1+%2B+2%2A%28y%5E2-8y%2B+16%29 = 12


From (2), substitute and replace (y2 - 8y) by 4x-16. You will 

      x%5E2+%2B+2x+%2B+1+%2B+2%2A%284x-16%2B+16%29 = 12.

Simplify

     x%5E2+%2B+2x+%2B+1+%2B+8x = 12,

     x%5E2+%2B+10x+-+11 = 0.

Factor left side and get

     (x+11)*(x-1) = 0.

The roots are x = -11 and x = 1.


From this point, complete the assignment on your own.

Solved.

For similar prototypes/samples see the lesson
    - Solving the system of algebraic equations of degree 2
in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Systems of equations that are not linear".