A person is remodeling the front entrance to his home and needs to cut an arch for the top of an entranceway. The arch needs to be \( 36 \mathrm{ft} \) wide and \( 6 \mathrm{ft} \) high. To draw the arch, he will use a stretched string with chalk attached at an end as a compass.
a) Using a coordinate system, locate the center of the circle
b) What radius should the person use to draw the arch?
a) The center of the circle is \( (0,-24) \).
(Type an ordered pair.)
b) To draw the arch, the person should use a radius of [ (Type an integer or a fraction.)
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Answer

\( r = \frac{\sqrt{1296 + 36}}{2} \)

Steps

Step 1 ：\( (x - 0)^2 + (y + 24)^2 = r^2 \)

Step 2 ：\( r^2 = 36^2 + 6^2 \)

Step 3 ：\( r = \frac{\sqrt{1296 + 36}}{2} \)