SOLUTION: Hello there, I am currently working on a math problem that I am struggling with. Please help me solve the following problem: Use completing the square to write the standard fo

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Question 1186650: Hello there,
I am currently working on a math problem that I am struggling with. Please help me solve the following problem:
Use completing the square to write the standard form of the expanded equation
10y^2-8x^2+80x+60y-190=0
___________=1
Thanks so much for your help!
-Diana
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
10y%5E2-8x%5E2%2B80x%2B60y-190=0
10y%5E2%2B60y-8x%5E2%2B80x-190=0
10%28y%5E2%2B6y%29-8%28x%5E2-10x%29=190

For the y's you need to use %286%2F2%29%5E2=9
and for the x's you need to use %2810%2F2%29%5E2=25.
Add them correspondingly INSIDE the grouping symbols. And add the same quantities which result from the remultiplications to the right hand side.

10%28y%5E2%2B6y%2B9%29-8%28x%5E2-10x%2B25%29=190%2B10%2A9-8%2A25

10%28y%2B3%29%5E2-8%28x-5%29%5E2=80
but this is not yet finished as an answer. You should be able to continue and then to finish.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Hello there,
I am currently working on a math problem that I am struggling with. Please help me solve the following problem:
Use completing the square to write the standard form of the expanded equation
10y^2-8x^2+80x+60y-190=0
___________=1
Thanks so much for your help!
-Diana
matrix%281%2C3%2C+10y%5E2+-+8x%5E2+%2B+80x+%2B+60y+-+190%2C+%22=%22%2C+0%29
 ------ Rearranging GIVEN equation, and moving CONSTANT to right-side
 
 --- Taking ½ of b on x, also ½ of b on y,                                   
                                                                                                squaring EACH result, then adding to
                                                                                                both sides   
 
 
matrix%281%2C3%2C+10%28y+%2B+3%29%5E2+-+8%28x+-+5%29%5E2%2C+%22=%22%2C+80%29 
matrix%281%2C3%2C+10%28y+%2B+3%29%5E2%2F80+-+8%28x+-+5%29%5E2%2F80%2C+%22=%22%2C+80%2F80%29 ---- Dividing by 80 in order to make right-side, 1
Simplifying entire equation gives us:

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

At this site,  there are many similar solved problems for conic sections: ellipses,  hyperbolas,  parabolas.

Below is the list of relevant lessons for ellipses and hyperbolas,  separated by types of conics

    - General equation of an ellipse
    - Transform a general equation of an ellipse to the standard form by completing the square

    - General equation of a hyperbola
    - Transform general equation of a hyperbola to the standard form by completing the square

Look into the lessons and learn the entire subject from there.

Consider them as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.