Question

question 1 of 10
what is the equation of the circle with center (-3.2, 2.1) and radius 4.3?
a. (x + 3.2)^2+(y - 2.1)^2 = 4.3^2
b. (x - 3.2)^2+(y + 2.1)^2=(4.3)^2
c. (x - 2.1)^2-(y + 3.2)^2=(4.3)^2
d. (x + 2.1)^2+(y - 3.2)^2 = 4.3^2

Explanation:

Step1: Recall circle - equation formula

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 values of \(h\), \(k\), and \(r\)

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

Step3: Substitute values into formula

Substitute \(h=-3.2\), \(k = 2.1\), and \(r = 4.3\) 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:

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