Question

Find the center of the circle whose equation is (x² - 10x + 25) + (y² - 16y + 64) = 16.

a.(10, 16) b.(5, 8) c.(-5, -8)

Answer 1

It’s b because we have (x-5)^2 + (y-8)^2=4^2. The center is (5,8) and r is 4

Answer 2

Option b is correct

(5, 8)

Explanation:

The general equation of circle with center (h, k) and radius r is given by:

`(x-h)^2+(y-k)^2 = r^2` ....[1]

As per the statement:

Given the equation:

`(x^2-10x+25) + (y^2 - 16y + 64) = 16`

then;

`(x^2-2 \cdot x \cdot 5+5^2) + (y^2 - 2 \cdot y \cdot 8 + 8^2) = 4^2`

Using identity rule:

`(a-b)^2 = a^2-2ab+b^2`

then;

`(x-5)^2+(y-8)^2 = 4^2`

Compare with equation [1];

h = 5 and k = 8

Therefore, center of circle, (5, 8)