# Circle, Circle Equations: Problems with Solutions

Problem 1
What is the center and radius of the circle $x^{2}+(y-3)^{2}=49$?
Graph the equation.
Problem 2
What is the center and radius of the circle $(x+2)^{2}+y^{2}=36$?
Problem 3
Complete the square and determine the center and radius of the circle $2x^{2}+2y^{2}+4x+16y+1=0$.
Problem 4
Which of the following is the equation of the circle with center at $(2,3)$ and radius $4$? Graph the equation.
Problem 5
Which of the following is the equation of the circle with
center at $(-1, 4)$ and a radius of 4? Graph the equation.
Problem 6
The center and radius of the circle $x^{2}+y^{2}-4x+2y=0$ is:
Problem 7
Which of the following lines is the tangent to the circle $x^{2}+y^{2}-4x-21=0$ at the point $T(5,4)$?
Problem 8
What is the equation of a circle with center at $(0,0)$ that passes through $(-1,-2)$?
Problem 9
What is the equation of a circle with center at $(4,-5)$ that passes through $(7,-3)$?
Problem 10
A circle with center at $(5,6)$ touches x-axis. What is the equation of the circle?

Problem 11
A circle with center at $(-4,3)$ touches y-axis.
What is the equation of the circle?
Problem 12
Find the equation of the circle with center $O(-2,3)$ and radius $r=4$. Which of the following points belong to the circle?
Problem 13
What is the equation of the circle with center $O(2,-1)$ that is tangent to the straight line $r:y=x+2$?
Graph the equation.
Problem 14
What is the equation of the circle concentric with circle $(x-2)^{2}+(y+1)^{2}=5$ that is tangent to the line $2x-y+2=0$?
Problem 15
Which of the following straight lines is a tangent to the circle $(x-2)^{2}+y^{2}=25$?

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