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Home >> Math Homework Help >> Calculus Homework >> Algebraic Curves Asymptotes
The equation of an algebraic curve of degree n is of the form (a_{0}x^{n} + a_{1}x^{n-1} y + … + a_{n} y^{n}) + (b_{0}x^{n-1} + b_{1}x^{n-2} y + …. + b_{n-1} y^{n-1}) + … + (ax + by) + c = 0. This can be written as Where is a polynomial in of degree r. Asymptotes parallel to the co-ordinate axes Let the equation of the curve be written as y^{n} Ø(x) + y^{n-1} Ø_{1}(x) + y^{n-2 }Ø_{2}(x) + … + yØ_{n-1} (x) + Ø_{n} (x) = 0, (1) where Ø(x), Ø_{1}(x), ……, Ø_{n}(x) are polynomials in x. Dividing (1) by y^{n}, we obtain Let x = a be a vertical asymptote of (1) so that y = ±∞, now it follows from (2), Ø(a) = 0. Therefore, ‘a’ is not root of Ø(x) = 0 which implies that (x – a) is a factor of Ø(x). Hence we have the following: Rule 1: The vertical asymptotes or the asymptotes parallel to the y-axis of an algebraic curve are obtained by equating to zero the real linear factors on the coefficient of the highest power of y in the equation of the given curve. Similarly, we have Rule 2: The horizontal asymptotes or the asymptotes parallel to the x-axis of an algebraic curve are obtained by equating to zero the real linear factors in the coefficient of the highest power of x in the equation of the given curve. Services: - Algebraic Curves Asymptotes Homework | Algebraic Curves Asymptotes Homework Help | Algebraic Curves Asymptotes Homework Help Services | Live Algebraic Curves Asymptotes Homework Help | Algebraic Curves Asymptotes Homework Tutors | Online Algebraic Curves Asymptotes Homework Help | Algebraic Curves Asymptotes Tutors | Online Algebraic Curves Asymptotes Tutors | Algebraic Curves Asymptotes Homework Services | Algebraic Curves Asymptotes