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circle has a diameter of 12 units, and its center lies on the x-axis. What could be the equation of the circle? Check all that apply.
(x – 12)2 + y2 = 12(x – 6)² + y² = 36x² + y² = 12x² + y² = 144(x + 6)² + y² = 36(x + 12)² + y² = 144

Answer :

Answer:  The correct options are

(B) [tex](x-6)^2+y^2=36,[/tex]

(D) [tex](x+6)^2+y^2=36.[/tex]

Step-by-step explanation:  Given that a circle has a diameter of 12 units and its center lies on the X-axis.

We are to select the equations that could be the equation of the circle.

The STANDARD equation of a circle with center at (h, k) and radius 'r' units is given by

[tex](x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Since the center of the circle lies on the X-axis, so the y co-ordinate will be zero.

That is, the center of the circle is of the form (h, 0).

Also, since the diameter of the circle is 12 units, so its radius will be

[tex]r=\dfrac{12}{2}=6~\textup{units}.[/tex]

Therefore, from equation (i), we get

[tex](x-h)^2+(y-0)^2=6^2\\\\\Rightarrow (x-h)^2+y^2=36~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Option (A) is

[tex](x-12)^2+y^2=12.[/tex]

Here, center = (12, 0), which lies on the X-axis and radius is

r = √12 ≠ 6 units.

So, this option is not correct.

Option (B) is

[tex](x-6)^2+y^2=36.[/tex]

Here, center = (6, 0), which lies on the X-axis and radius is

r = √36 = 6 units.

So, this option is correct.

Option (C) is

[tex]x^2+y^2=12.[/tex]

Here, center = (0, 0), which lies on the X-axis and radius is

r = √12 ≠ 6 units.

So, this option is not correct.

Option (D) is

[tex](x+6)^2+y^2=36.[/tex]

Here, center = (-6, 0), which lies on the X-axis and radius is

r = √36 = 6 units.

So, this option is correct.

Option (E) is

[tex](x+12)^2+y^2=144.[/tex]

Here, center = (-12, 0), which lies on the X-axis and radius is

r = √144 = 12 ≠ 6 units.

So, this option is not correct.

Thus, the correct options are

(B) [tex](x-6)^2+y^2=36,[/tex]

(D) [tex](x+6)^2+y^2=36.[/tex]

facundo3141592

We want to see which ones of the given equations can represent a circle of a diameter of 12 units that lies on the x-axis.

The correct options are the second and fourth ones:

  • (x – 6)² + y² = 36
  • (x + 6)² + y² = 36.

The general equation of a circle of radius R, that lies on the point (a, b) is given by:

(x - a)^2 + (y - b)^2 = R^2

Now, if we want it to be on the x-axis, then we must have b = 0. And if the diameter (remember that the diameter is twice the radius) is 12 units, then:

2*R = 12

R = 12/2 = 6

So the equation will be something like:

(x - a)^2 + y^2 = 6^2 = 36

So we just need to see whose of the given equations have this general form. These are the second and fourth options:

  • (x – 6)² + y² = 36
  • (x + 6)² + y² = 36.

If you want to learn more about circles, you can read:

https://brainly.in/question/32281344

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