How do I simplify an equation with the form x^2 -y^2 +ax +by +c into two brackets ie: (x+y+k)(x+y+c)?

[Andohr]

I have a question that wants me to prove an equation in the general form for a circle is equal to two brackets each containing an x term, a y term and a constant.

 

From what I understand this is an equation of a circle. I've tried to put it into the standard equation of a circle and working from there, I've tried factorizing the like terms and I can't seem to get anywhere. I've been tried using the quadratic equation with respect to x but with no luck either.

 

Any pointers are appreciated a lot. If I've tried the right strategy and just made a silly error please notify me.

[studiot]

Welcome Andohr.

 

Since no one else seems to want to help, although there were plenty logged in who could have.

 

You need to recast your thread title to correct algebraic expressions. The question is impossible as you have written it. (you need a way to make the coefficient of y² negative)

 

Then multiply out the two expressions (x+y+k)(x+y+j) (there i've done a bit for you already) and 'compare coefficients'

 

That is form a set of simultaneous equations comparing the terms in your other expression with the result of your multiplication, amd solve them/

 

For instance jk = c is one.

 

By the way none of your expressions are actually equations since they do not contain an equals sign- just a small point.

 

Edited October 13, 2014 by studiot

[fiveworlds]

x^2 -y^2 +ax +by +c

(x+y+k)(x+y+c)=x^2+yx+kx+y^2+yx+yk+cx+cy+ck

x^2 -y^2 +ax +by +c =x^2+yx+kx+y^2+yx+yk+cx+cy+ck

-y^2 +ax +by +c =yx+kx+y^2+yx+yk+cx+cy+ck

ax+by+c=yx+kx+2y^2+yx+yk+cx+cy+ck

by+c=yx+kx+2y^2+yx+yk+cx+cy+ck-ax

by=yx+kx+2y^2+yx+yk+cx+cy+ck-ax-c

b=yx+kx+2y^2+yx+yk+cx+cy+ck-ax-c/y

 

x^2 -y^2 +ax +yx+kx+2y^2+yx+yk+cx+cy+ck-ax-c +c=(x+y+k)(x+y+c)

[imatfaal]

I have a question that wants me to prove an equation in the general form for a circle is equal to two brackets each containing an x term, a y term and a constant.

 

From what I understand this is an equation of a circle. I've tried to put it into the standard equation of a circle and working from there, I've tried factorizing the like terms and I can't seem to get anywhere. I've been tried using the quadratic equation with respect to x but with no luck either.

 

Any pointers are appreciated a lot. If I've tried the right strategy and just made a silly error please notify me.

 

How do I simplify an equation with the form x^2 -y^2 +ax +by +c into two brackets ie: (x+y+k)(x+y+c)?

 

ok. firstly to re-iterate above - they are not equations!

 

if you set each equal to zero then the general form of the circle is not how you have it; that's a hyperbola. take a look at some references to find the general form - youre close but vital incorrect signs.

 

The bracketed versions are not a circle either - they are closer to section of a parabolic cylinder.

 

There is a bracketed version of the circle and we can go over that if you find the other version