Question

the pythagorean theorem can be modified in relationship to an oval shape or ellipse. in this modified form, the square of the major axis (a) equals the sum of the square of the minor axis (b) and the square of the focus (c). because of their unique locations, the endpoints of the focus provide ideal locations for symmetry for decorations, per a custom order for a cake. if the cake is ordered in an elliptical shape with a major axis of 12 inches and a minor axis of 6 inches, how far along the major axis from the center in either direction (i.e., the focus) will the decorations need to be placed?
$a^{2}=b^{2}+c^{2}$
find c when a = 12 and b = 6.
(you do not need to include the units. only enter the number value for an answer. round to the nearest tenth if necessary.)

Explanation:

Step1: Substitute values into formula

Given \(a^{2}=b^{2}+c^{2}\), substitute \(a = 12\) and \(b = 6\). So, \(12^{2}=6^{2}+c^{2}\).

Step2: Simplify the equation

\(144=36 + c^{2}\). Then, \(c^{2}=144 - 36\).

Step3: Calculate \(c^{2}\)

\(c^{2}=108\).

Step4: Solve for \(c\)

\(c=\sqrt{108}\approx10.4\)

Answer:

\(10.4\)