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What is the standard form of the equation of the circle in the graph?

A(x - 1)2 + (y - 2)2 = 4
B(x + 1)2 + (y + 2)2 = 4
C(x + 1)2 + (y + 2)2 = 16
D(x - 1)2 + (y - 2)2 = 16

What is the standard form of the equation of the circle in the graph? A. (x - 1)2 + (y - 2)2 = 4 B. (x + 1)2 + (y + 2)2 = 4 C. (x + 1)2 + (y + 2)2 = 16 D. (x - class=

Verified Answer :

D. (x - 1)2 + (y - 2)2 = 16
Remember the circle formula: (x-h)^2 +(y-k)^2 = r^2

Answer: The correct option is (D) \((x-1)^2+(y-2)^2=16.\)

Step-by-step explanation:  We are given to select the standard form of the equation of the circle in the graph.

We know that

the standard  form of the equation of a circle with center at (h, k) and radius r units is given by

\((x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)

From the graph, we see that

the center of the circle at the point (1, 2).

That is, (h, k) = (1, 2).

The radius is the distance between the center and any point on the circumference of the circle. So, the radius of the circle as calculated from the graph is

r = 4 units.

Substituting the value of (h, k) and r in equation (i), we get

\((x-1)^2+(y-2)^2=4^2\\\\\Rightarrow (x-1)^2+(y-2)^2=16.\)

Thus, the required standard equation of the circle is \((x-1)^2+(y-2)^2=16.\)

Option (D) is correct.