Question

Which equation represents the circle described?

The radius is 2 units.
The center is the same as the center of a circle whose equation is x2 + y2 – 8x – 6y + 24 = 0.
(x + 4)2 + (y + 3)2 = 2

(x – 4)2 + (y – 3)2 = 2
(x – 4)2 + (y – 3)2 = 2²
(x + 4)2 + (y + 3)2 = 2²

Answer 1

Answer: the answer is C :)

Answer 2

ANSWER


`{(x - 4)}^(2) + {(y - 3)}^(2) = {2}^(2)`

Step-by-step explanation

The equation of the circle with radius r and centre (a,b) is given by



`(x - a)^(2) + {(x - b)}^(2) = {r}^(2)`

The radius is


`r = 2`

We need to determine the center of the circle from the given equation of another circle, which is,



`{x}^(2) + {y}^(2) - 8x - 6y + 24 = 0`


We complete the square to obtain,



`{x}^(2) - 8x+ {y}^(2) - 6y + 24 = 0`


`{x}^(2) - 8x+ {y}^(2) - 6y = - 24`

`{x}^(2) - 8x+ {( - 4)}^(2) + {y}^(2) - 6y + {( - 3)}^(2) = - 24 + {( - 3)}^(2) + {( - 4)}^(2)`



`{(x - 4)}^(2) + {(y - 3)}^(2) = - 24 + 9+ 16`





`{(x - 4)}^(2) + {(y - 3)}^(2) = 1`


The centre of this circle is (4,3)


Hence the center of the circle whose equation we want to find is also (4,3).


With this center and radius 2, the required equation is,



`{(x - 4)}^(2) + {(y - 3)}^(2) = {2}^(2)`


Therefore the correct answer is C.