SOLUTION: Solve the system and graph the curves: b) 9x^2+4y^2+18x-16y = 0 ; and (x+1)^2+2(y-4)^2 = 12

Question 1048625: Solve the system and graph the curves:
b) 9x^2+4y^2+18x-16y = 0 ; and
(x+1)^2+2(y-4)^2 = 12
Answer by ikleyn(52810) (Show Source): You can put this solution on YOUR website!
.
Solve the system and graph the curves:
9x^2 + 4y^2 + 18x - 16y = 0,
(x+1)^2 + 2(y-4)^2 = 12.
~~~~~~~~~~~~~~~~~~~~~~~~~

Open parentheses in the second equation. Then the system is equivalent to

9x^2 + 18x     + 4y^2 - 16y = 0,            (1)

 x^2 +  2x + 1 + 2y^2 - 16y + 32 = 12.      (2)


Multiply the equation (2) by 9 (both sides). You ill get

 9x^2 + 18x + 9 + 18y^2 - 144y + 288 = 108.    (3)

Now distract equation (1) from equation (3). You will get

14y^2 - 128y + 9 + 288 = 108,

14y^2 - 128y + 189 = 0.

Next solve this quadratic equation for "y" and then find the appropriate solutions for "x".

For solution of similar problems see the lesson
- Solving systems of algebraic equations of degree 2
in this site.

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