1. Write the equation of a circle in that passes through the point (5 , 4) and has a center at (2 , 0)

2. Find the center and radius of a circle with equation:
x2 − 6x + y2 + 10y = 2

3. Find the center and radius of the circle with equation:
x2 − 10x + y2 − 8y = − 32

4. Write the equation of a circle if the endpoints of the diameter are (—5, 6) and (1, —2)

5. Find the point on x-axis which is equidistant from (-2,5) and (2,3)

6. Classify the triangle A(-1, 2), B(4, 2), and C(3, -1) by sides.

7. Determine whether the points A(0, 5), B(0, -5), and C(-3, 3) are the vertices of a right triangle.

8. The midpoint of segment AB is M(3, —6). One endpoint is A(—4, —5 )
The midpoint of segment AB is M(3, —6). One endpoint is A(—4, —5 ). Find the coordinates of the other endpoint B.

9. The parallelogram PQRS has coordinates P(2,3), Q (8,1), and R(11,5)
The parallelogram PQRS has coordinates P(2,3), Q (8,1), and R(11,5). What are the coordinates of point S?

10. Find the equation of the line tangent to the circle x2 + y2 = 25 at (3,4)

11. Find the intersection of the circles
x2 + y2 = 4 and x2 + y2 - 4x - 4y = -4
Answer: (2, 0) and (0, 2)

12. Find the distance between the centers of the circles x2 + y2 + 8x + 7= 0 and
x2 +y2—2x +4y – 4 = 0