Question

question 21 of 25
the graph of the equation below is a circle. what is the length of the radius of the circle?
$(x + 5)^{2}+(y + 7)^{2}=21^{2}$
a. 42
b. 441
c. 10.5
d. 21

Explanation:

Step1: Recall the standard form of a circle 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: Compare with the given equation

Given \((x + 5)^2+(y + 7)^2=21^2\). Here \(r^2 = 21^2\).

Step3: Find the radius

Taking the square root of \(r^2\), we get \(r=\sqrt{21^2}=21\).

Answer:

D. 21