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so what they're asking us to do in this
equation is to write the equation of the
circle so the main important thing to
write the equation of the circle we have
to know what is the general equation of
circle which was in your notes last
class period guillermo
and that equation is x minus h squared
plus
y minus k
squared equals r squared so right to
write the equation of the circle we need
to know the center and the radius
right because remember the center
is in form of h k
and the radius
is equal to r
all right so we go and look at our
general equation and we say all right
are we provided what the center is
or do we need to find it yeah we pride
at the center that's just h and k
right perfect
do we know the radius
yeah no no we're not provided the radius
right so in this problem we're not
providing the radius however if i
plugged in numbers for x and h and y and
k
would it make sense that i could solve
for a variable r
yes so i know h and k that's provided to
us
but it what could i use for x and y
a point on the circle which they give us
right
remember if you guys look at a circle
graphed that's the center
h comma k any point that i say is on
this circle
is a coordinate point which can
represent x y the equation of the circle
represents infinite many points amani on
the circle so therefore i can say that's
x y
so now all i need to do ladies and
gentlemen is plug those points in and
solve for r
so x is 4
minus 5
squared plus y which is 0. now here's
where you got to be careful
it's y minus k right
y
minus
what is k
so it's going to be a positive all right
equals r squared
well 4 minus 5 is 1 1 squared is 1
plus
negative 2 minus 2 is going to or
negative 2 minus 2 is positive positive
4
equals r squared 5 equals r squared
four minus five that's all it's gonna be
for that so five squared is there if i
asked you what the radius was you could
say the radius is the square root of 5.
all right but we're not really talking
about what r is we don't really care
actually what the r is we just want to
know what the equation of the circle is
so the radius of square root of 5 you
square that and it's just equal to 5. so
now that i know the center can i plug
those in for h and k and now that i know
what r squares can i plug that in and
that's the equation of my circle
so therefore i have x
minus 5
squared
plus
y plus 2 squared equals 5.
notice how it's the opposite it's
opposite h opposite k since h is
positive it's x minus h
since at k is negative it's y plus 2
right so it's the opposite of those and
then we figured out r squared which was
5.
any other questions on that
okay
good talk
