Linear Equations and Circles
This page covers fundamental concepts of linear equations and circles in analytical geometry.
Linear Equations
The page begins with the explicit and implicit forms of linear equations. It introduces the formula retta passante per due punti equationofalinepassingthroughtwopoints:
Formula: y - y₁ = y2−y1/x2−x1 * x−x1
The coefficiente angolare retta passante per due punti slopeofalinepassingthroughtwopoints is also provided:
Formula: m = y2−y1/x2−x1
Other important concepts include:
- Midpoint formula
- Distance between two points
- Distance from a point to a line
Highlight: The page emphasizes the relationship between parallel lines sameslope and perpendicular lines slopesarenegativereciprocalsofeachother.
Circles
The section on circles introduces the general equation of a circle:
Formula: x−x0² + y−y0² = r²
Where x0,y0 is the center and r is the radius.
The implicit form of the circle equation is also presented:
Formula: x² + y² + ax + by + c = 0
The page concludes with information on the family of circles and degenerate circles.
Vocabulary: A degenerate circle is a circle with a radius of zero, which reduces to a point.