What is the standard equation of the circle that is tangent to both coordinate axes, lies in the second quadrant, and has an area of $36\pi$ square units?

A) $(x - 6)^2 + (y + 6)^2 = 36$

B) $(x + 6)^2 + (y - 6)^2 = 36$

C) $(x + 6)^2 + (y - 6)^2 = 6$

D) $(x - 6)^2 + (y - 6)^2 = 36$

A circle with center $(4, -3)$ is tangent to the vertical line $x = -1$. What is the standard equation of this circle?

A) $(x + 4)^2 + (y - 3)^2 = 25$

B) $(x - 4)^2 + (y + 3)^2 = 25$

C) $(x - 4)^2 + (y + 3)^2 = 9$

D) $(x + 4)^2 + (y - 3)^2 = 9$

A) $(x + 1)^2 + (y - 1)^2 = 25$

B) $(x - 1)^2 + (y + 1)^2 = 100$

C) $(x - 1)^2 + (y + 1)^2 = 25$

D) $(x + 1)^2 + (y - 1)^2 = 100$

A) Center $(3, -5)$ and radius $5$

B) Center $(-3, 5)$ and radius $5$

C) Center $(3, -5)$ and radius $25$

D) Center $(-3, 5)$ and radius $\sqrt{19}$

A) $(x - 3)^2 + (y + 5)^2 = 25$

B) $(x + 3)^2 + (y - 5)^2 = 25$

C) $(x + 3)^2 + (y - 5)^2 = 5$

D) $(x - 3)^2 + (y + 5)^2 = 5$

Math · Geometry · Math · Circles

5 Math practice questions on Equation of a circle. Questions that assess core concepts and understanding.

1.
What is the standard equation of the circle that is tangent to both coordinate axes, lies in the second quadrant, and has an area of $36\pi$ square units?
- A) $(x - 6)^2 + (y + 6)^2 = 36$
- B) $(x + 6)^2 + (y - 6)^2 = 36$
- C) $(x + 6)^2 + (y - 6)^2 = 6$
- D) $(x - 6)^2 + (y - 6)^2 = 36$
2.
A circle with center $(4, -3)$ is tangent to the vertical line $x = -1$ . What is the standard equation of this circle?
- A) $(x + 4)^2 + (y - 3)^2 = 25$
- B) $(x - 4)^2 + (y + 3)^2 = 25$
- C) $(x - 4)^2 + (y + 3)^2 = 9$
- D) $(x + 4)^2 + (y - 3)^2 = 9$
3.
A circle has a diameter with endpoints at $A(-3, 2)$ and $B(5, -4)$ . What is the standard equation of this circle?
- A) $(x + 1)^2 + (y - 1)^2 = 25$
- B) $(x - 1)^2 + (y + 1)^2 = 100$
- C) $(x - 1)^2 + (y + 1)^2 = 25$
- D) $(x + 1)^2 + (y - 1)^2 = 100$
4.
What are the center and the radius of the circle defined by the equation $x^2 + y^2 - 6x + 10y + 9 = 0$ ?
- A) Center $(3, -5)$ and radius $5$
- B) Center $(-3, 5)$ and radius $5$
- C) Center $(3, -5)$ and radius $25$
- D) Center $(-3, 5)$ and radius $\sqrt{19}$
5.
What is the standard equation of the circle with center $(-3, 5)$ that passes through the point $(1, 2)$ ?
- A) $(x - 3)^2 + (y + 5)^2 = 25$
- B) $(x + 3)^2 + (y - 5)^2 = 25$
- C) $(x + 3)^2 + (y - 5)^2 = 5$
- D) $(x - 3)^2 + (y + 5)^2 = 5$