Example Problems with Circle Equations

This page presents practical applications of circle equations through example problems, reinforcing the concepts of równanie okręgu postać ogólna (general form of circle equation) and methods to wyznacz środek i promień okręgu (determine the center and radius of a circle).

The first problem demonstrates how to find the center of a circle given its equation:

Example: Given the circle equation (x+3)² + (y-4)² = 25, find the coordinates of the center S. Solution: Comparing with the standard form (x-a)² + (y-b)² = r², we can deduce that a=-3 and b=4. Therefore, S(-3,4).

The second problem introduces a more complex scenario involving two circles:

Example: Find the distance between the centers of circles with equations (x+1)² + (y-2)² = 9 and x² + y² = 10.

This problem requires identifying the centers of both circles and then applying the distance formula between two points.

Vocabulary: The środek okręgu wzór (circle center formula) can be derived by comparing the given equation to the standard form (x-a)² + (y-b)² = r².

These examples provide valuable practice in working with równanie okręgu zadania pdf (circle equation problems) and reinforce the importance of understanding both the general and canonical forms of circle equations.