Answer:
B, B, and C
Step-by-step explanation:
1. We see that the center is (-1, 2) and the point the circle goes through is
(2, -2). We can use the distance formula to figure out the radius:
r = [tex]\sqrt{(-1-2)^2+(2-(-2))^2} =\sqrt{(-3)^2+(4)^2} =\sqrt{9+16} =\sqrt{25} =5[/tex]
Diameter = 2 * radius = 2 * 5 =10. Thus, the answer is B.
2. According to the equation, we can find the center and radius. The generic formula of a circle is: [tex](x-h)^2+(y-k)^2=r^2[/tex] , where h is the x coordinate of the center, k is the y coordinate of the center, and r is the radius.
Here, we see that h = 2, k = 1, and r^2 = 9 so r = 3. Look for an answer choice that matches this description. Only B matches, so that's the answer.
3. We see that the diameter is from (5, 4) to (-1, -4), so let's use the distance formula to figure out the length:
d = [tex]\sqrt{(5-(-1))^2+(4-(-4))^2} =\sqrt{(6)^2+(8)^2} =\sqrt{100} =10[/tex].
So, since d = 10, then r = 5 (because the radius is 1/2 of the diameter)
With just this information, we can just look at the answer choices. The correct answer should be the one where the right side is equal to r^2 = 5^2 = 25. Only C matches, so that's the answer.
The answers are B, B, and C.
Hope that helps!
