The equation of a circle with center at (h,k) and radius r is:
In your first example, you could re-write the equation as
Therefore h = 0 and k = 0 so the center is at (0,0) and the radius is 10
The second example is a trivial application of what I just showed you,
so you can do that one yourself.
The third one has the slight twist that, so
The fourth one is a bit trickier. You need to complete the square for each of the variables
First rearrange:
Now, what constant, p, do you need to add so thatis a perfect
square? Let's try 4.. So add 4 to both sides of
the equation.
Next, look at the y terms. If we add 1,, so add 1 to
both sides of the equation.
Collect terms on the right, and factor the x and y parts of the left
Remember the minus signs in the standard circle equation,
That means we need to re-write the x part:
Now we have the circle's parameters directly: Center at (-2,1), radius = 3
Using the process I just showed you for the fourth example, you should be able
to solve the fifth one as soon as you determine whether the equal sign between
theand terms should be a plus sign or a minus sign.
(Did you hit the adjacent key or forget to shift?)
Hope that helps,
John