Question

set

1. circle a is centered at the origin. each of the four right triangles inside ⊙a has a hypotenuse that measures

8 units. write the equation of ⊙a.

1. let

Explanation:

Step1: Recall the standard equation of a circle

The standard equation of a circle with center \((h,k)\) and radius \(r\) is \((x - h)^2+(y - k)^2=r^2\).

Step2: Identify the center and radius

Since the circle \(A\) is centered at the origin \((0,0)\) (so \(h = 0,k = 0\)) and the radius \(r\) is equal to the length of the hypotenuse of the right - triangle which is \(8\) units.
Substitute \(h = 0,k = 0,r = 8\) into the standard equation: \((x-0)^2+(y - 0)^2=8^2\)

Answer:

\(x^{2}+y^{2}=64\)