General Form of an equation

**JudaStar** · February 27th 2009, 06:19 PM

(x-3)^2+(y+4)^2=25

This is the Standard Form of the equation. How do I convert it into the General Form of this equation? I am working with circles, grafting etc. I was given the center and radius and ask to find the standard form of the equation and the general form of the equation. I cannot understand how to convert the standard form (above) into the general form of the equation.

**ADY** · February 28th 2009, 08:58 AM

Ok

$(x-3)^2 +(y+4)^2 = 25$ X

$(x-3)(x-3)$
$X x X, X x 3, 3 x X, 3 x 3$
$X^2, 3X, 3X, 9$
$X^2, 6X, 9$

$(y+4)(y+4)$
$y x y, y x 4, 4 x y, 4 x 4$
$y^2, 4y, 4y, 16$
$y^2 + 8y + 16$

Check 16 + 9 = 25

Hope that helps
ADY

**stapel** · February 28th 2009, 12:20 PM

Originally Posted by JudaStar

I do not know what "expand the brackets" means

To "expand" the squares of the parenthesized expressions, multiply them out and then simplify the result. For instance:

. . . . . $(x\, +\, 3)^2\, +\, (y\, -\, 1)^2\, =\, 9$

. . . . . $(x\, +\, 3)(x\, +\, 3)\, +\, (y\, -\, 1)(y\, -\, 1)\, =\, 9$

. . . . . $x^2\, +\, 6x\, +\, 9\, +\, y^2\, -\, 2y\, +\, 1\, =\, 9$

. . . . . $x^2\, +\, y^2\, +\, 6x\, -\, 2y\, +\, 10\, =\, 9$

. . . . . $x^2\, +\, y^2\, +\, 6x\, -\, 2y\, +\, 1\, =\, 0$

**mr fantastic** · February 28th 2009, 12:58 PM

Originally Posted by stapel

To "expand" the squares of the parenthesized expressions, multiply them out and then simplify the result. For instance:

. . . . . $(x\, +\, 3)^2\, +\, (y\, -\, 1)^2\, =\, 9$

. . . . . $(x\, +\, 3)(x\, +\, 3)\, +\, (y\, -\, 1)(y\, -\, 1)\, =\, 9$

. . . . . $x^2\, +\, 6x\, +\, 9\, +\, y^2\, -\, 2y\, +\, 1\, =\, 9$

. . . . . $x^2\, +\, y^2\, +\, 6x\, -\, 2y\, +\, 10\, =\, 9$

. . . . . $x^2\, +\, y^2\, +\, 6x\, -\, 2y\, +\, 1\, =\, 0$

*Sigh* Another assumption it's no longer safe to make ....

What is actually getting taught in the classroom these days (perhaps the question should be what is being learned in the classroom these days)? Very little, it seems.

**JudaStar** · March 1st 2009, 01:53 PM

Thanks to ADY, Stapel, and Mr fantastic for helping. I had to take my final exam for College Algebra on Saturday morning, before the help from these postings. There was only a couple of questions dealing with this and I could give the standard form of the equation. So I did ok. Well, really ok. I MADE 100 ON MY FINAL. Yahoo!! That was my last class for my degree. I saved the algebra until my last course, because I dreaded it so. I am a microcomputer and web design major. By the grace of God, much study, and stress I will have an A in the course and I never intend to talk to algebra again.

Thanks again,
Juda Star

Thread: General Form of an equation

LinkBack

Thread Tools

Display

General Form of an equation

Thank you

Similar Math Help Forum Discussions

Writing transform. form of a quad. function in the general form?

find the general form of the equation of each circle

Write an equation of the circle described in both the standard form and general form

Graphing an ellipse given its equation in general form

Search Tags