Question

The equation of a circle is (x−11) ²+(y+15) ²=144.

(a) Johnny said that the center of the circle is located at (15, -11). Is Johnny correct? Explain your answer.




Joyce said that the diameter of the circle is 144 units. Is Joyce correct? Explain your answer

Answer 1

For this case we have that by definition, the general equation of the circle is given by:

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

Where,

• (h, k): it is the center of the circle
• r: radius of the circle

We then have the following equation:

`(x-11) ^ 2 + (y + 15) ^ 2 = 144`

Comparing values ​​we have:

For the center of the circle :

`(h, k) :( 11, -15)`

For the radius:

`r ^ 2 = 144\\r = \sqrt {144}\\r = 12`

Then, the diameter is given by:

`d = 2r\\d = 2 (12)\\d = 24`

Answer:

Johnny is wrong:

The center of the circle is (11, -15)

Joyce is wrong:

The diameter of the circle is 24