Question

1. which of the following is the equation in standard form of a circle with center (8, 0) and radius equal to 5 ?

a. $(x - 5)^2 + (y + 8)^2 = 0$
b. $\frac{(x)^2}{5} + \frac{(y + 8)^2}{5} = 25$
c. $(x - 8)^2 + (y)^2 = 25$
d. $(x + 8)^2 + (y - 5)^2 = 64$
e. $(5x + 8)^2 + (5y)^2 = 125$
f. $(x - 8)^2 + (y)^2 = 10$
g. $sqrt{(x)^2 + (y - 8)^2} = 25$

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is \((x - h)^2 + (y - k)^2 = r^2\).

Step2: Identify the values of \(h\), \(k\), and \(r\)

Given the center \((8, 0)\), so \(h = 8\) and \(k = 0\). The radius \(r = 5\), so \(r^2 = 5^2 = 25\).

Step3: Substitute the values into the standard form

Substituting \(h = 8\), \(k = 0\), and \(r^2 = 25\) into the standard form equation, we get \((x - 8)^2 + (y - 0)^2 = 25\), which simplifies to \((x - 8)^2 + y^2 = 25\).

Answer:

C. \((x - 8)^2 + (y)^2 = 25\)