Question

What is the center of the circle given by the equation (x + 5)2 + (y - 8)2 = 1?

A. (-5, 8)
B. (-5, -8)
C. (5, 8)
D. (5, -8)

Answer 1

A. The centre of the circle is: (-5, 8)

Answer 2

Answer: The correct option is (A) (-5, 8).

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

`(x+5)^2+(y-8)^2=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that

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

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

From equation (i), we have

`(x+5)^2+(y-8)^2=1\\\\\Rightarrow (x-(-5))^2+(y-8)^2=1^2.`

Comparing the above equation with the standard form, we get

center, (h, k) = (-5, 8).

Thus, the required center of the given circle is (-5, 8).

Option (A) is CORRECT.