2. Juanita is asked to write the standard equation of a
circle with center (-2, 3) that passes through the point
(-2, 6). Is Juanita's equation correct? Explain.
Juanita's equation: (x + 2)2 – (y + 3)2 = 9

It is not.  Also use ^2 to represent squaring a number.  

Step-by-step explanation:

First, USE ^2 FOR SQUARED

It is not correct.

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

In your question the center is (-2,3) and the radius is the length of the line segment from the center to any pointon the circle.  nd hey, it tells us a point on the circle is (-2,6).

Let's take it one part at a time.  we know h and k so let's plug them in.

(x-h)^2 + (y-k)^2

(x-(-2))^2 + (y-3)^2

(x+2)^2 + (y-3)^2

now r is the length of the line segment from (-2,3) and (-2,6).  To get from (-2,3) to (-2,6) hopefully it is pretty obvious you just move up (so int he y direction) 3 spaces.  this makes r = 3.  int he formula we want r^2 and that is 9.  The result is that the circle has a formula of:

(x-h)^2 + (y-k)^2 = r^2

(x+2)^2 + (y-3)^2 = 9

The formula Juanita got is actually a hyperbola.  

3, 12, 48, 384, 1536, 6144, 24576, 98304

step-by-step explanation:

just keep timing it by 4.