Hough Transform can be used to extract lines from images. It can also be used to extract curves - this is a little harder though because higher dimensional Hough transforms
Do you only need to locate the curve for which you already know your parameters a,b,c? Using GHT you can create a discrete voting space from your eq. Use it to vote in a 2d space and you will find your curve. If your are trying to determine a,b,c from the Hough Transform it will be harder :)