SOLUTION: Please help!!! Determine values for A, B, and C such that the equation below represents the given type of conic. Each axis of the ellipse, parabola, and hyperbola should be horiz

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Please help!!! Determine values for A, B, and C such that the equation below represents the given type of conic. Each axis of the ellipse, parabola, and hyperbola should be horiz      Log On


   

Question 615277: Please help!!!
Determine values for A, B, and C such that the equation below represents the given type of conic. Each axis of the ellipse, parabola, and hyperbola should be horizontal or vertical. Then rewrite your equation for each conic in standard form, identify (h, k), and describe the translation.
Ax^2+By+Cy^2+2x-4y-5=0
Part A: Circle
Part B: Ellipse
Part C: Parabola
Part D: Hyperbola
Found 2 solutions by solver91311, jsmallt9:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If A = C, and neither is zero, you have a circle.

If A is not equal to C, and neither is zero, but they are both the same sign, then ellipse.

If A and C have different signs, and neither is zero, then hyperbola.

If either A or C is zero, but not both, then parabola.

If both A and C are zero, then straight line.


John

My calculator said it, I believe it, that settles it
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Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I'm pretty sure you mean:
Ax%5E2%2BBxy%2BCy%5E2%2B2x-4y-5=0+

You are asking for solutions to four problems, each one of which requires a substantial amount of work. All I'm going to to is help you get started. If this is not enough for you then re-post your problem in hopes someone is willing to do more.

My suggestions/thoughts:
  • A non-zero value for B makes the problems much more difficult. (A non-zero B tilts the graphs so that they are not horizontally or vertically oriented.) I suggest a value of zero for B for all four problems. Note: All of the following suggestions assume that the B is zero!
  • A value of zero for A or for C (but not both) will result in a parabola. I suggest a value of zero for C and a value of 1 for A for the parabola problem.
  • For circles, A = C. I suggest 1's for both.
  • If A and C have opposite signs you get a hyperbola. I suggest 1 for A and -1 for C
  • If A and C have the same sign but are not equal, you get an ellipse. I suggest 1 for A and 2 for B.
After you have entered your choices for A, Band C into the general equation, you will need to complete the squares. Complete the squares for both x and y terms in all equations except for the one for the parabola. The parabola equation will have just one squared term (since the coefficient for the other squared term is zero) so just complete the square for that variable.

After completing the square(es), then transform the equation into the proper forms:
  • Circle: %28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2
  • Ellipse: %28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1
  • Parabola: %28x-h%29%5E2+%2B+4p%28y-k%29 if C = 0 or
    %28y-k%29%5E2+=+4p%28x-h%29 if A = 0
  • Hyperbola: %28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1 if A > 0 or
    %28y-k%29%5E2%2Fa%5E2+-+%28x-h%29%5E2%2Fb%5E2+=+1 if B > 0