Question

question 6 of 10
what is the equation of the circle with center (3.2, -2.1) and radius 4.3?
a. (x + 2.1)^2 + (y - 3.2)^2 = 8.6
b. (x + 3.2)^2 + (y - 2.1)^2 = 4.3
c. (x - 2.1)^2 - (y + 3.2)^2 = (4.3)^2
d. (x - 3.2)^2 + (y + 2.1)^2 = (4.3)^2

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 \((3.2,-2.1)\), so \(h = 3.2\), \(k=-2.1\), and radius \(r = 4.3\).

Step3: Substitute into the standard form

Substitute \(h = 3.2\), \(k=-2.1\), \(r = 4.3\) into \((x - h)^2+(y - k)^2=r^2\).
We get \((x - 3.2)^2+(y-(-2.1))^2=(4.3)^2\), which simplifies to \((x - 3.2)^2+(y + 2.1)^2=(4.3)^2\).

Answer:

D. \((x - 3.2)^2+(y + 2.1)^2=(4.3)^2\)