SOLUTION: I need to convert this equation to standard form: 16x^2 + 4y^2 + 96x - 8y + 84 = 0 I know the standard form is x^2/a^2 + y^2/b^2 = 1 How do I begin?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I need to convert this equation to standard form: 16x^2 + 4y^2 + 96x - 8y + 84 = 0 I know the standard form is x^2/a^2 + y^2/b^2 = 1 How do I begin?      Log On


   

Question 195695: I need to convert this equation to standard form:
16x^2 + 4y^2 + 96x - 8y + 84 = 0
I know the standard form is x^2/a^2 + y^2/b^2 = 1
How do I begin?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I need to convert this equation to standard form:
16x^2 + 4y^2 + 96x - 8y + 84 = 0
I know the standard form is x^2/a^2 + y^2/b^2 = 1
How do I begin?
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Separate x's and y's
16x^2 + 96x + 4y^2 - 8y = -84
Complete the squares for x and y
(16x^2 + 96x + 144) + (4y^2 - 8y + 4) = -84 + 148
(4x + 12)^2 + (2y - 2)^2 = 64
16(x+3)^2 + 4(y-1)^2 = 64
(x+3)^2 + (y-1)^2/4 = 4
%28%28x%2B3%29%5E2%29%2F4+%2B+%28%28y-1%29%5E2%29%2F16++=++1
If that's not sufficient, email me via the thank you note.