SOLUTION: What would these equations be in standard form??? I know that this is a hyperbola - x^2-y^2-8x+10y+15=0 And this is a parabola - y^2+4y-8x+4=0

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: What would these equations be in standard form??? I know that this is a hyperbola - x^2-y^2-8x+10y+15=0 And this is a parabola - y^2+4y-8x+4=0      Log On


   



Question 391114: What would these equations be in standard form???
I know that this is a hyperbola - x^2-y^2-8x+10y+15=0
And this is a parabola - y^2+4y-8x+4=0

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Complete the square:



Constant to the RHS:



Group similar terms:



Divide the x-terms by the coefficient on . Since this is already 1, skip this step.

Divide the coefficent on the term by 2, square the result, then add that result to both sides of the equation. -8 divided by 2 is -4. -4 squared is 16. Add 16 to both sides.



Divide the y-terms by the coefficient on .




Divide the coefficent on the term by 2, square the result, then add that result to both sides of the equation. -10 divided by 2 is 5. 5 squared is 25. But consider the -1 coefficient in front of the parentheses. Add -25 to both sides.



Factor the two perfect square trinomials in the LHS and collect terms in the RHS.



Divide both sides by -24:



One problem per post, please.

John

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