Question

Which of the following is the representation of a plane algebraic curve of nth degree?

(a) f(x,y)=ay^n+(bx+c) y^n-1+(dx^2+ex+f) y^n-2+⋯+un (x)=0

(b) f(x,y)=ay^n-1+(bx+c) y^n-2+(dx^2+ex+f) y^n-3+⋯+un (x)=0

(c) f(x,y)=ay^n+by^n-1+cy^n-2+⋯+un (x)=0

(d) f(x,y)=ay^n+(bx+c) y^n+(dx^2+ex+f) y^n+⋯+un (x)=0

The question was asked in my homework.

Question is from Curves in Cartesian Form in division Curve Tracing of Engineering Mathematics

Answer 1

Correct answer is (a) f(x,y)=ay^n+(bx+c) y^n-1+(dx^2+ex+f) y^n-2+⋯+un (x)=0

Easiest explanation: Plane algebraic curve of nth degree is represented by,

f(x,y)=ay^n+(bx+c) y^n-1+(dx^2+ex+f) y^n-2+⋯+un (x)=0

Where a, b, c, d, e, f are all constants and un(x) is a polynomial in x of degree n.