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Meehan98

  • one year ago

Identify the standard form of the equation by completing the square. 3x^2 − 2y^2 − 12x − 16y + 4 = 0

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  1. Meehan98
    • one year ago
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    I know how to begin by factoring the 3 and -2 so you're left with: 3(x^2-4x+4) -2(y+8y+16)= -4

  2. Meehan98
    • one year ago
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    And the next step is to make the constants equal so you get: 3(x^2-4) - 2(y+8)= -24

  3. Jhannybean
    • one year ago
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    I would start like this: group the x and y terms separately: \((3x^2-12x) +(-2y^2-16y)+4=0\) Then i'd send 4 to the other side so i have all my variables on one side and my constants on the other: \((3x^2-12x)+(-2y^2+16y)=-4\) Factor out the LCM for both sets of ( ) on the LHS : \(3(x^2-4x)-2(y^2+8y)=-4\) The stuff inside the () is in the form \((ax^2+bx)\) So in order to complete the quadratic, we need to find new c values for both sets of ( ). We're goign to find \(c_1\) which correlates to the first set of ( ) and \(c_2\) which correlates to the second ( ) : \(c_1 = \left(\dfrac{-4}{2}\right)^2 = (-2)^2 = 4\) \(c_2 = \left( \dfrac{8}{2}\right)^2 = (4)^2 = 16\) Now we plug these in to the ( ) respectively : \(3(x^2-4x\color{red}{+4})-2(y^2+8y\color{blue}{+16})=-4\) But now here's the problem child, you have to remember whatever you do on the LHS you also have to do on the RHS. because we pulled out the LCMs \(3\) and \(-2\), we're going to multiply both \(c_1\) and \(c_2\) with these LCMs and add them on the RHS: \(3(x^2-4x\color{red}{+4})-2(y^2+8y\color{blue}{+16}=-4\color{red}{+12} \color{blue}{-32} \)

  4. Jhannybean
    • one year ago
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    Now we just simplify both the LHS and RHS : \(3(x-2)^2 -2(y+4)^2 = -24\) this completes the standard form of the equation: \((x-h)^2+(y-k)^2=r^2\)

  5. Jhannybean
    • one year ago
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    \(3(x^2-4x\color{red}{+4})-2(y^2+8y\color{blue}{+16})=-4\color{red}{+12} \color{blue}{-32}\)* fixed a typo.

  6. Meehan98
    • one year ago
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    Okay, I just realized that I typed in a different answer than what I originally had, and I had the same answer as you and that's why I was confused because these are my choices for the correct answer.

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  7. Jhannybean
    • one year ago
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    Okay, let me see, one minute.

  8. Meehan98
    • one year ago
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    Ah, I got it! (y+4)^2/12 - (x-2)^2/8 =1 because you divide -24 to both sides!

  9. Jhannybean
    • one year ago
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    Yeah :D

  10. Jhannybean
    • one year ago
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    It's asking for the elliptical form

  11. Meehan98
    • one year ago
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    You're amazing! Thanks for your help!!!!

  12. Jhannybean
    • one year ago
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    No problem. Did you understand my explanation, or were there any questions about it?

  13. Meehan98
    • one year ago
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    Nope, I understood it perfectly!

  14. Jhannybean
    • one year ago
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    Nice :D

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