Question

Two circles are concentric if they have the same center. on a coordinate plane, a circle has center (4, 6) and has a radius of 2 units. 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

The equation, which represents a circle that is concentric with the circle shown and has a radius twice as large of that circle, is (x-4)²+(y-6)²=16.

What is the equation of circle?

The equation of the circle is the equation which is used to represent the circle in the algebraic equation form, with the value of center point in the coordinate plane and measure of radius.

The standard form of the equation of the circle can be given as,

$(x-h)^2+(y-k)^2=r^2$

Here (h,k) is the center of the circle and (r) is the radius of the circle.

On a coordinate plane, a circle has a center (4, 6) and has a radius of 2 units.

The equation of another circle which is concentric with the circle has to be found out. Two circles are concentric if they have the same center.

Thus, the center of this circle is also (4,6). Now, this circle has a radius that is twice as large. Thus, the radius of this circle is,

$r=2\times2\\r=4$

The equation of this circle with center (4,6) and radius 4 is,

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

Thus, the equation, which represents a circle that is concentric with the circle shown and has a radius twice as large as that circle, is (x-4)²+(y-6)²=16.

Learn more about the equation of circle here;

https://brainly.com/question/1506955

Answer 2

Answer: (x – 4)2 + (y – 6)2 = 16

Step-by-step explanation: i took the test n got it correct :)