Odredi dvije tockw koje leze na kruznici sa sredistem (3,-1) i polumjerom 2

To solve this problem, we need to find two points that lie on a circle with a given center and radius. Let's break down the problem and solve it step by step.

1. Break Down the Problem

   We are given:

   • The center of the circle: $C(3, -1)$
   • The radius of the circle: $r = 2$

   We need to find two points $(x, y)$ that satisfy the equation of the circle.

2. Relevant Concepts

   The equation of a circle with center $(h, k)$ and radius $r$ is given by: $(x - h)^2 + (y - k)^2 = r^2$ Substituting the given values: $(x - 3)^2 + (y + 1)^2 = 4$

3. Analysis and Detail

   We can choose specific values for $x$ or $y$ to find corresponding points on the circle. Let's choose $x = 3$ and solve for $y$.

   • Substituting $x = 3$ into the circle equation: $(3 - 3)^2 + (y + 1)^2 = 4$ $0 + (y + 1)^2 = 4$ $(y + 1)^2 = 4$ Solving for $y$: $y + 1 = \pm 2$ $y = 1 \quad \text{or} \quad y = -3$

   Thus, the points are $(3, 1)$ and $(3, -3)$.

4. Verify and Summarize

   We can verify these points by substituting them back into the circle equation:

   • For $(3, 1)$: $(3 - 3)^2 + (1 + 1)^2 = 0 + 4 = 4$
   • For $(3, -3)$: $(3 - 3)^2 + (-3 + 1)^2 = 0 + 4 = 4$

   Both points satisfy the circle equation.

Final Answer

The two points that lie on the circle are $(3, 1)$ and $(3, -3)$.