Equation of a circle Knowledge-Based Practice

Questions

1. 1.

   Which of the following is the standard equation of the circle that is concentric with the circle $x^2 + y^2 - 8x + 2y + 8 = 0$ and has an area of $25\pi$?

   • A) $(x - 4)^2 + (y + 1)^2 = 25$
   • B) $(x + 4)^2 + (y - 1)^2 = 25$
   • C) $(x - 4)^2 + (y + 1)^2 = 5$
   • D) $(x + 4)^2 + (y - 1)^2 = 5$
2. 2.

   What is the standard equation of the circle with center $(4, -3)$ that is tangent to the $x$-axis?

   • A) $(x - 4)^2 + (y + 3)^2 = 9$
   • B) $(x - 4)^2 + (y + 3)^2 = 16$
   • C) $(x + 4)^2 + (y - 3)^2 = 9$
   • D) $(x + 4)^2 + (y - 3)^2 = 16$
3. 3.

   What is the standard equation of the circle that has a diameter with endpoints $A(-1, 2)$ and $B(5, -6)$?

   • A) $(x + 2)^2 + (y - 2)^2 = 25$
   • B) $(x - 2)^2 + (y + 2)^2 = 25$
   • C) $(x - 2)^2 + (y + 2)^2 = 100$
   • D) $(x + 2)^2 + (y - 2)^2 = 100$
4. 4.

   What are the center and radius of the circle defined by the equation $x^2 + y^2 - 6x + 8y - 11 = 0$?

   • A) Center $(3, -4)$ and radius $6$
   • B) Center $(-3, 4)$ and radius $6$
   • C) Center $(3, -4)$ and radius $36$
   • D) Center $(-6, 8)$ and radius $\sqrt{11}$
5. 5.

   What is the standard equation of the circle with center $(-3, 4)$ that passes through the point $(1, 1)$?

   • A) $(x - 3)^2 + (y + 4)^2 = 25$
   • B) $(x + 3)^2 + (y - 4)^2 = 5$
   • C) $(x + 3)^2 + (y - 4)^2 = 25$
   • D) $(x - 3)^2 + (y + 4)^2 = 5$

Answers and step-by-step solutions appear after you finish the test.