Question

Two circles are concentric if they have the same center. Which equation represents a circle that is concentric with the circle shown but has a radius that is twice as large? (x – 4)2 + (y – 6)2 = 4 (x – 4)2 + (y – 6)2 = 16 (x – 6)2 + (y – 4)2 = 16 (x – 6)2 + (y – 4)2 = 4

Answer 1

`(x-4)^2 + (y-6)^2 = 16`

Explanation:

Just to clarify the answer

Answer 2

Since you did not include the figure with the circle to which you have to compare the equations, I am going to determine the center and radius of the circles represented by each of the equations.

From that, you choose that whose center is the same of your circle and the radius is the double.


The canonic equation of a circle is:

(x - a)² + (y - b)² = r²

Where a and b are the coordinates of the center (a,b) and r is the radius.

So, let's determine the center and the radius of all the equations given:

A) (x – 4)² + (y – 6)² = 4


Center (4,6),;radius = √4 = 2


B) (x – 4)² + (y – 6)² = 16


Center (4, 6); radius = √16 = 4


C) (x – 6)² + (y – 4)² = 16


Center = (6, 4); radius = √16 = 4


D) (x – 6)² + (y – 4)² = 4

Center (6, 4); radius = √4 = 2