Question

name date unit 2, lesson 9 - ready, set, go ready factor. 1. $b^{2}-49$ 5. $25 x^{2}-49 y^{2}$ 2. $b^{2}-2 b + 1$ 6. $36 x^{2}+60 x y + 25 y^{2}$ 3. $x^{2}-y^{2}$ 7. $81 a^{2}-16 d^{2}$ 4. $9 x^{2}-66 x y + 121 y^{2}$ 8. $144 x^{2}-312 x y + 169 y^{2}$ set 10. circle a is centered at the origin. each of the four right triangles inside $odot a$ has a hypotenuse that measures 8 units. write the equation of $odot a$.

Explanation:

Step1: Recall the equation of a circle

The standard equation of a circle centered at the origin \((0,0)\) is \(x^{2}+y^{2}=r^{2}\), where \(r\) is the radius.

Step2: Find the radius

For a right - triangle with hypotenuse \(h = 8\) (the distance from the origin to a point on the circle, which is the radius). By the Pythagorean theorem, if the legs of the right - triangle are \(a\) and \(b\), and the hypotenuse \(r\) (since the circle is centered at the origin, the hypotenuse of the right - triangle is the radius of the circle). Here \(r = 8\)

Answer:

The equation of \(\odot A\) is \(x^{2}+y^{2}=64\)