Question

find an equation for the circle.
center at (9,0), radius 10

a. $x^2 + (y + 9)^2 = 10$
b. $(x + 9)^2 + y^2 = 100$
c. $x^2 + (y - 9)^2 = 10$
d. $(x - 9)^2 + y^2 = 100$

Explanation:

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

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

Step2: Identify \(h\), \(k\), and \(r\)

Given center \((9,0)\), so \(h = 9\), \(k = 0\), and radius \(r = 10\).

Step3: Substitute values into the formula

Substitute \(h = 9\), \(k = 0\), \(r = 10\) into \((x - h)^2+(y - k)^2=r^2\).
We get \((x - 9)^2+(y - 0)^2=10^2\), which simplifies to \((x - 9)^2+y^2 = 100\).

Answer:

D. \((x - 9)^2+y^2 = 100\)