Module 7: Conics
Lesson 1 Notes
Part 1: Circles
Video 1 Transcript
Hey everyone this is a video for module 7 lesson 1, Circles Notes part 1.
So in the notes about circles, you learned that the standard equation of a circle is “x”
minus “h” squared plus “y” minus “k” squared equals “r” squared. The center of the
circle is going to be ( h, k) and the radius is “r.” So in the first couple of examples, we
are going to state the radius, state the center and the radius. So if I look at this
equation, and I look at the standard form up here. We did this a couple of times in
the notes. If I have a plus 4 there and my standard equation has a minus, and there’s
a minus and to get that to be a positive, there would have had to be a negative 4 in
for the “h” value. Since this is a minus and this is a minus, I would have had to
subtract a positive 5 there. This value right here is “r” squared is 49 so “r” would be
a value of 7. You don’t’ have to put the plus or minus since this is going to be a
distance. So right here I could rewrite the 49 to be 7 squared. So to rewrite this,
now I can see that the “h” value is a negative 4, and my “k” value is a 5. So the center
is going to be (-4, 5) and the radius is going to be 7. So as you can see I manipulated
this to find the “h” and “k.” A lot of people will just look right here and if they know
it’s a circle they take the opposite of that sign which is -4 and the opposite of that
sign which would be positive 5.
Ok, looking at the second example if I have “x” minus 3 squared plus “y” minus 1
squared equals 70 squared. Then I know the center there if I take the opposite of
this its going to be 3, the opposite of this would be 1. The radius is going to be the
square root of this, since “r” squared is 70, then “r” would be the square root of 70.
So the radius of that would be the square root of 70.
Ok, looking at the next example it says graph the following circles. So if you look at
this the first thing we need to do is get the center. The center since there is nothing
with the x it would be 0 comma take the opposite of that it would be 5. Since this is
“r” squared “r” squared is 25, which means my radius would be 5. So I am going to
go ahead and graph the center there. The center is going to be (0,5), with the radius
of 5. So I would go up 5, 1, 2, 3, 4, 5, go over 5, to the left 5 and down 5. To draw my
circle there, I would go out from there. Let me do that over, and that would be your
circle. So the center of (0,5) and then your radius.
Ok, the next equation says, “x” minus 1 squared plus “y” plus 3 squared equals 15.
So we know that my center is (1, -3) because it is going to be the opposite of this and
the opposite of this. (1, -3) would be here. 15, “r” squared equals 15, so that means
that the “r” would equal the square root of 15 since that is not the exact answer. I
am going to do 15 raise to the half, because that is the same thing as square rooting,
taking the square root of 15. So that is approximately 3.87.
So about 4, so lets see 3.87 is the radius that is 1, 2, 3 and there 4 about 87 (.87). Of
course this is not going to be exact but we can get pretty close. Let me try that one
more time. And there is your circle.