Question

The center of a circle represented by the equation (x − 5)2 + (y + 6)2 = 42 is

Answer 1

(5,-6)

Explanation:

When you write the equation of a circle in the form

`(x-x_0)^2+(y-y_0)^2=r^2`

Then the center of the circle will be
`(x_0,y_0)` and the radius will be
`r`.

Answer 2

Answer: The center of the given circle is (5, -6).

Step-by-step explanation: We are given to find the center of the circle represented by the following equation :

`(x-5)^2+(y+6)^2-4^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that

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

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

From equation (i), we have

`(x-5)^2+(y+6)^2=4^2\\\\\Rightarrow (x-5)^2+(y-(-6))^2=4^2.`

Comparing with the standard form, we get that the center of the given circle is (h, k) = (5, -6).

Thus, the center of the given circle is (5, -6).