Question

17.1 equation of a circle
example = 2
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
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

Explanation:

Step1: Recall circle equation formula

The standard equation of a circle 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 \(r\) for part b

For part b, center is \((0,12)\) so \(h = 0\), \(k = 12\), and radius \(r=2.5\). Then \(r^2=(2.5)^2 = 6.25\).

Step3: Substitute into the formula

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:

B. \(x^2+(y - 12)^2 = 6.25\) (assuming the option with this equation is the second one in the list)