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