okay let's do some math for fun and here's the question for you guys as you can see on the
screen right here we have two circle looking circles and my question for you guys is that
which one it's actually a circle the red one with a blue one what do you guys think well maybe
both well maybe neither and you guys can click it on but the button right there so you can vote
right all right so that was round one because you might be thinking hey we didn't have enough
information so don't worry here is wrong too and let me help you guys out a little bit and as you
can see i have the x and y axis for you guys and they are still the same thing from earlier okay
and let me tell you guys that the answer is that the blue one is not a circle as you can see on
the blue one right here just pay attention to the middle well it goes from negative two to positive
4 right so that's 6. however if you focus on the x axis it goes from negative 3 to positive 3
and that's also 6 and the problem is that that x-axis length right there is not the main diameter
for sure because it's not in the middle therefore it's not a circle right in fact the red one is a
circle this right here is the polar equation and i will convince you guys that this right here is
indeed a circle so now let's see first thing first r's are 2 is 2 but for this sine theta
we can write it as y over r and similarly we'll just continue plus 6 and for cosine you have
to remember it's x over r now this is very nice because we can multiply everybody by r and when
we do that r times r is of course r squared and that's equal to just two y here and then just plus
6x and now notice we have the r squared which is the same as saying x squared plus y squared
isn't it yeah and then of course we still have this 2y plus 6x from here we can actually just
move these two terms to the other side and complete the square and you'll see this is
in fact a circle in the cartesian form right so here we go this is x square i will pair up with
minus 6x after i move this to the other side leave a space for the magic number and then i will add
y square minus 2y and then leave a space and this is equal to 0 right here
okay notice that we have a one right here so that's good go ahead and use the formula right
this right here is negative six we have to take one half of negative six and then we square that
and that's negative 3 squared we get positive 9 so i'm going to add 9 here and add 9 here this
is the magic number it's so magical once you add it here you complete the square right okay here
we do the same thing we are going to take half of this so half of negative 2 and square that
this is going to give me negative 1 square so that's actually positive add the positive 1
on both sides again matching number works out so magically because as you can see this right here
it's actually x minus 3 squared and this right here is y minus 1 squared this right here is
of course 10. as you can see this right here is in fact an equation of a circle with the center
at 3 comma 1 and the radius is this is 10 but you look at the square root of 10 squared so the
radius is actually square root of 10 which is approximately 3 point something right
anyway this right here is it this is how you work with polar equations okay before we go i
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it's a circle but it seems that i have another circle on my back
anyway hopefully you guys all like this video and as always that's it
you