Question

Another conics question. (Need tutored, no idea about conics).

Answer 1

Find the center and radius of a circle that has a diameter with endpoints(-9,-6) and (-1,0).

Answer 2

hmm here we go
bty you can google "conics purplemath" and get real good explanations

Answer 3

oh i will google that too c:

Answer 4

ok first you need the center of the circle, which is another way of saying you need to find the midpoint of the line segment

Answer 5

Isnt it (-9)+1 / (-6)-0?

Answer 6

you need help with that, or is it clear how to find the midpoint?

Answer 7

oh no, i think you have the midpoint confused with the "slope" which has nothing to do with this problem

Answer 8

Oh yeah.. I cant remember the midpoint formula /:

Answer 9

the midpoint is just the average of each coordinate

Answer 10

i.e. add up and divide by 2

Answer 11

add up x and x? or x and y?

Answer 12

\[\frac{-9-1}{2}=\frac{-10}{2}=-5\] for the \(x\)

Answer 13

so -5,-3?

Answer 14

\(x\) and \(x\) for the \(x\)
\(y\) and \(y\) for the \(y\)

you cannot add or subtract \(x\) and \(y\) they live in different

yes

Answer 15

now we area half way done
the general form is
\[(x-h)^2+(y-k)^2=r^2\] and you have \(h=-5, k=-3\)

Answer 16

and the radius is half of the diameter, so (-5,-3) to -1,0) is the radius, so I have to use the distance formula?

Answer 17

so far we know the equation is going to look like
\[(x+5)^2+(y+3)^2=r^2\]

Answer 18

yes exactly you have to use the distance formula to find \(r\) but before you do, notice that you really need \(r^2\) and not \(r\) so you can use the distance formula without the square root

Answer 19

in other words compute
\[(-1+5)^2+3^2\]

Answer 20

25

Answer 21

i hope that is clear, that will give you \(r^2\) which is what you want
i get \(4^2+3^2=25\)

Answer 22

right

Answer 23

now you are done

Answer 24

But is the radius 25 units or 5 units?

Answer 25

\[(x+5)^2+(y+3)^2=25\]

Answer 26

the radius is \(r\) and since \(r^2=25\) you know \(r=5\)

Answer 27

Makes perfect sense! Thank you again c:

Answer 28

yw

Answer 29

you can send the cookie in the mail

Answer 30

Haha c: