Question

multiple-choice question try b.: what is the equation of the circle? $x^2 + (y - 12)^2 = 2.5$ $x^2 + (y - 12)^2 = 6.25$ $x^2 - (y + 12)^2 = 6.25$ $(x - 12)^2 + y^2 = 6.25$ rewatch 17.1 equation of a circle write the standard equation of the circle with the given center and radius. a. center $(5, -8)$, radius 6 $(x - h)^2 + (y - k)^2 = r^2$ $(x - 5)^2 + (y - (-8))^2 = 6^2$ $(x - 5)^2 + (y + 8)^2 = 36$ b. center $(0, 12)$ and radius 2.5

Explanation:

Step1: Recall the standard 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: Identify the center and radius

For this problem, the center is \((0, 12)\) (so \(h = 0\), \(k = 12\)) and the radius \(r = 2.5\). First, calculate \(r^2\): \(r^2=(2.5)^2 = 6.25\).

Step3: Substitute into the standard equation

Substitute \(h = 0\), \(k = 12\), and \(r^2 = 6.25\) into \((x - h)^2 + (y - k)^2 = r^2\). We get \((x - 0)^2+(y - 12)^2=6.25\), which simplifies to \(x^2+(y - 12)^2 = 6.25\).

Answer:

\(x^2+(y - 12)^2 = 6.25\) (the second option in the multiple - choice list)