1

Recently I came across this question, where the top voted answer claimed that all homogeneous equation represent a set of straiight lines passing through origin. I was wondering if this was true generally, and if so, how can we prove this?

Soumik Mukherjee
  • 746
  • 1
  • 5
  • 15
Eisenstein
  • 435
  • Hint: What can you say about the constant term of a homogeneous equation? – Soumik Mukherjee Jul 14 '23 at 06:09
  • @SoumikMukherjee I know that the constant term of homogeneous equation is 0 thus implying the curves pass through origin. But why does it have to represent a set of straight lines? Can you please elaborate? – Eisenstein Jul 14 '23 at 06:23
  • 1
    If $(x,y)$ is a point on the curve then $(\lambda x,\lambda y)$ is also a point on the curve for any real $\lambda$. So for each point (other than the origin) on the curve, you are getting the line through that point and origin also on the curve. – Soumik Mukherjee Jul 14 '23 at 06:39
  • 1
    @SoumikMukherjee Got it! Many thanks:) – Eisenstein Jul 14 '23 at 06:56

0 Answers0