Question

question 9 of 10
the circle below is centered at the point (-1, 2) and has a radius of length 3.
what is its equation?
a. $(x - 1)^2+(y + 2)^2 = 9$
b. $(x - 2)^2+(y + 1)^2 = 3^2$
c. $(x + 2)^2+(y - 1)^2 = 3^2$
d. $(x + 1)^2+(y - 2)^2 = 9$

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 the center and radius

Given the center \((-1,2)\), so \(h=-1\), \(k = 2\), and radius \(r = 3\).

Step3: Substitute into the standard form

Substitute \(h=-1\), \(k = 2\), \(r = 3\) into \((x - h)^2+(y - k)^2=r^2\).
We get \((x-(-1))^2+(y - 2)^2=3^2\), which simplifies to \((x + 1)^2+(y - 2)^2=9\).

Answer:

D. \((x + 1)^2+(y - 2)^2=9\)