Algebra Graphing Problem: x^2 + y^2 + 4x + 6y = 32
- Thread starter jjdevi1
- Start date
Let's complete the square.
Group like terms:
\(\displaystyle (x^{2}+4x+?)+(y^{2}+6y+?)=32\)
We must find out what the question marks represent by taking half the coefficient of x, squaring it, and adding it to both sides.
The coefficient of x in the first one is 4, half of that is 2, sqaure that is 4.
The other is half of 6 squared, which is 9.
We have:
\(\displaystyle \L\\(x^{2}+4x+4)+(y^{2}+6y+9)=32+9+4=45\)
Factor:
\(\displaystyle \L\\(x+2)^{2}+(y+3)^{2}=45\)
Now, can you see what it is?.
Group like terms:
\(\displaystyle (x^{2}+4x+?)+(y^{2}+6y+?)=32\)
We must find out what the question marks represent by taking half the coefficient of x, squaring it, and adding it to both sides.
The coefficient of x in the first one is 4, half of that is 2, sqaure that is 4.
The other is half of 6 squared, which is 9.
We have:
\(\displaystyle \L\\(x^{2}+4x+4)+(y^{2}+6y+9)=32+9+4=45\)
Factor:
\(\displaystyle \L\\(x+2)^{2}+(y+3)^{2}=45\)
Now, can you see what it is?.
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- Feb 4, 2004
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Trying to tutor through an "interpreter" who doesn't know the "language" is, in my experience, unlikely to be successful. So please have your son reply, showing what he has tried and where he is stuck.jjdevi1 said:
For instance, since these equation types and shapes have been covered in class, he has learned the basic relationships:
. . .Are both variables squared?
. . . . .No: It's a parabola.
. . . . .Yes:
. . . . . . .Do the two squared variables have the same sign?
. . . . . . . . .No: It's an hyperbola.
. . . . . . . . .Yes:
. . . . . . . . . . .Do the two squared variables have the same coefficient?
. . . . . . . . . . . . .No: It's an ellipse.
. . . . . . . . . . . . .Yes: It's a circle.
I realize that the above probably doesn't make any sense to you, but it should be very familiar to him. Please have him reply, showing where he is stuck in the sorting process.
Thank you.
Eliz.