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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