Question

1. true or false the radius of the circle x² + y² = 9 is 3. 6. true or false the center of the circle (x + 3)² + (y - 2)² = 13 is (3, -2).

Explanation:

Step1: Recall circle - standard form

The standard form of a circle is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center and $r$ is the radius.

Step2: Analyze the first circle $x^{2}+y^{2}=9$

For the circle $x^{2}+y^{2}=9$, we can rewrite it as $(x - 0)^2+(y - 0)^2 = 3^2$. So the radius $r = 3$. The statement is True.

Step3: Analyze the second circle $(x + 3)^2+(y - 2)^2=13$

For the circle $(x + 3)^2+(y - 2)^2=13$, comparing with the standard - form $(x - a)^2+(y - b)^2=r^2$, we have $a=-3$ and $b = 2$. So the center is $(-3,2)$ not $(3,-2)$. The statement is False.

Answer:

1. True
2. False