Which equation represents a circle is concentric with the circle shown but has a radius that is twice as large?

Equation of a cercle: (x-h)² + (y-k)² = R², where h and k are the center O of the circle, O(h , k)
The equation of the circle shown is:
(x-4)² + (y-6)² = 2² =4
A cercle concentric to the above, should have the same center as the above, but the radius should be greater to 4.
In your given answers only (x-4)² + (y-6)² = 16 satisfies the question.
So (x-4)² + (y-6)² = 16 is the concentric with (x-4)² + (y-6)² =4

Answer Link

Anshuyadav Anshuyadav · Answer 2 · 2022-07-19T19:17:34+02:00

The equation of the concentric circle is [tex](x-4)^{2} +(y-6)^{2} =16[/tex].

What is the general equation of the circle?

The general equation of the circle is given by

[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex].

Where,

(h, k) is the center of the circle

and, r is the radius of the circle

What is concentric circle?

The circles with a common center are known as concentric circles and have different radii.

According to the given question.

We have a graph, in which a circle is drawn with center (4, 6) and radius 2.

Therefore, the equation of the concentric circle that has the a radius is twice as large to the given circle is

[tex](x-4)^{2} +(y-6)^{2} = (2\times 2)^{2}[/tex]

[tex]\implies (x-4)^{2} +(y-6)^{2} = (4)^{2}[/tex]

[tex]\implies (x-4)^{2} +(y-6)^{2} =16[/tex]

Hence, the equation of the concentric circle is [tex](x-4)^{2} +(y-6)^{2} =16[/tex].

Find out more about the equation of circle and concentric circle here:

https://brainly.com/question/6614262

#SPJ2