3
$\begingroup$

I'm trying to work on a problem, and I'm stuck at simplifying this equation. I do not why I cannot see it:

so the book gives the following equation:

$$\frac{ax}{x^2+y^2}+\frac{by}{x^2+y^2}+c=0$$

where c is nonzero.

Now the book simplifies it like this:

$$x^2+y^2+\frac{a}{c} x+\frac{b}{c} y=0$$

Does anyone know how they simplified it? I believe they divided c, but I do not know how $x^2+y^2$ disappeared

Also, this involves the equation of a circle

$\endgroup$
7
$\begingroup$

Hint: multiply both sides by $x^2 + y^2$ to clear the fractions, then simplify.

$\endgroup$
  • $\begingroup$ alright, thanks! lemme try right now. $\endgroup$ – kero Mar 9 '15 at 5:29
  • 1
    $\begingroup$ You can also bring the equation to standard form by completing square. $\endgroup$ – MathMajor Mar 9 '15 at 5:30
  • $\begingroup$ I got it. Thanks a lot! $\endgroup$ – kero Mar 9 '15 at 5:31
  • $\begingroup$ Don't forget either x or y needs to be strictly positive. $\endgroup$ – Pierre Arlaud Mar 9 '15 at 9:08
  • $\begingroup$ @Rohinb97, I was but they don't let you accept it right away D: $\endgroup$ – kero Mar 10 '15 at 0:35

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.