The point where two curves meet is called a point of intersection. In coordinate geometry, this is the coordinate (x,y)(x,y)(x,y) that lies on both curves at the same time.

What “point where two curves meet” means

When two graphs share a common point, they are said to intersect at that point. At this point of intersection, both curves have the same xxx value and the same yyy value, so they represent the same position on the plane.

  • It can be where two straight lines cross.
  • It can be where a line and a curve touch.
  • It can be where two general curves meet one or more times.

If they just touch once and do not cross, the point is still an intersection, and in calculus it is often also a tangent point.

How to find the point where two curves meet

To find the point(s) where two curves meet, you treat it like solving two equations at once.

  1. Write both equations with yyy (or the same expression) on one side, for example:
    • Curve 1: y=f(x)y=f(x)y=f(x)
    • Curve 2: y=g(x)y=g(x)y=g(x).
  1. Set them equal: f(x)=g(x)f(x)=g(x)f(x)=g(x).
  1. Solve this equation for xxx; each solution gives an xxx-coordinate of an intersection.
  1. Substitute each xxx back into either original equation to get the corresponding yyy.

Example from a forum-style explanation: if y=2x2y=2x^2y=2x2 and y=x2+1y=x^2+1y=x2+1, set them equal: 2x2=x2+12x^2=x^2+12x2=x2+1, which simplifies to x2−1=0x^2-1=0x2−1=0, giving x=1x=1x=1 or x=−1x=-1x=−1. Plugging back gives intersection points (1,2)(1,2)(1,2) and (−1,2)(-1,2)(−1,2).

Quick terminology snapshot

Here’s a compact view of related phrases:

html

<table>
  <tr>
    <th>Phrase</th>
    <th>What it usually means</th>
  </tr>
  <tr>
    <td>Point of intersection</td>
    <td>The point where two lines or curves meet on a graph.[web:1][web:3]</td>
  </tr>
  <tr>
    <td>Intersection point(s)</td>
    <td>One or more coordinates shared by both graphs.[web:1][web:5]</td>
  </tr>
  <tr>
    <td>Tangent point</td>
    <td>A special intersection where curves touch but do not cross.[web:10]</td>
  </tr>
</table>

Mini “story” example

Imagine two companies: one curve shows cost and the other shows revenue as production increases. Where those two curves meet, the company’s revenue equals its cost, so that intersection point on the graph is the break-even point.

In many economics and business discussions, people literally look for “the point where the two curves meet” on a chart—because that single dot often decides profit, loss, or balance.

Bottom note

Information gathered from public forums or data available on the internet and portrayed here.

TL;DR: The point where two curves meet is called a point of intersection , and you find it by setting their equations equal and solving for the shared coordinates.