Question

Write the equation of the circle with center (0, 0) and radius = 14.

A) x^2 + y^2 = 14

B) x^2 + y^2 = 196

C) (x - 0)^2 + (y - 0)^2 = 14^2

D) (x + 0)^2 + (y + 0)^2 = 14^2

Answer 1

The equation of a circle with center (0, 0) and radius 14 is x² + y² = 196, which corresponds to option B in the provided choices.

Thus, the correct option is B.

Step-by-step explanation:

To write the equation of a circle with center (0, 0) and radius = 14, we use the standard form of the circle's equation, which is (x - h)² + (y - k)² = r² where (h, k) is the center of the circle and r is the radius. Since the center is at the origin (0, 0) and the radius is 14, we plug these values into the equation to get:

(x - 0)² + (y - 0)² = 14²

Which simplifies to:

x² + y² = 196

This corresponds to option B of the multiple-choice answers provided. Remember that the squared radius in the equation of a circle is a very common place for mistakes, so always square the radius correctly to get the right equation.