Question

http://prntscr.com/6ruct9

Answer 1

Find the slope first: \(\sf \color{red}{\frac{y_2-y_1}{x_2-x_1}}\)
then use \(\sf (y_0 -y_1)=m(x_0-x_1)\)

Answer 2

m = slope
You can pick ANY \(\sf \color{red}{one}\) point to plug into x\(_1\) and \(\sf y_1\)

Answer 3

aren't we going to use the formula? (x-h)^2=(y-k)=r^2

Answer 4

Ye matey, that is the formula we need to use, only you will need + between the x and y brackets

Answer 5

oh yeah, forgot to put the +

Answer 6

\[(x-h)^2 \space + \space ( y-k)^2 \space = r^2\]

Answer 7

alright, how do I make the circle?

Answer 8

do you mean draw it?

Answer 9

You will need to identify the elements for it first. You need the center and the radius
the center is already given as (-1, -3) so that means the h and k values are the coordinates of the center ...

h is -1 and k is -3 here

Answer 10

so you will have to plug in those values into the equation
as well as the given point, the (3, 0) point and from that, you will end up with an equation, from which you can solve for the radius

Answer 11

so that'd be, (x-(-1)^2 + (y-(-3)^2=r^2 ?

Answer 12

ye, that is correct so far ... go on

Answer 13

\[(x-(-1)^2 + (y-(-3)^2=r^2 \]

Answer 14

um then (x-1)^2 + (y+3)^2=r^2

Answer 15

the first bracket should be (x+1)
\[ (x+1)^2 + (y+3)^2=r^2\]

Keep going ...

Answer 16

oh ok, and then

d= that root symbol (x,+1{down2})^2 + (y,y4{down 2}^2

Answer 17

You don't need that, you are given the point (3, 0) on the circle
so you can plug in that point into the equation you already have, the (x+1)^2 + (y+3)^2 = r^2

Answer 18

oh...then what is the next step?

Answer 19

you need to plug in the given point into the equation
you have to replace the X with 3 and the Y with 0 and try and solve for the r from that, savvy?

Answer 20

(3+1)^2 + (0-3)^2 =r^2 ?

Answer 21

the signs inside the brackets are +s
the -s got cancelled earlier, there are no more -s

Answer 22

(3+1)^2 + (0+3)^2 =r^2 like this? and what is "s"?

Answer 23

\[(3+1)^2 \space + (0+3)^2 \space = r^2\]
Can you try and continue with that to solve for the r ?

Answer 24

\(\color{blue}{\text{Originally Posted by}}\) @tanya123
(3+1)^2 + (0+3)^2 =r^2 like this? and what is "s"?
\(\color{blue}{\text{End of Quote}}\)
That's right! The S is minuses, the minus signs you had earlier got cancelled, there are no more minuses, -s is just a short name for minuses, savvy? :)

Answer 25

lol oh, thanks!

and is r 25^2? so 625?

Answer 26

Ahoy, Matey ... let me show you how the calculations work like:
\[4^2+3^2 \space = r^2\]
\[16+9 = r^2\]
\[\sqrt{25} \space = \sqrt{r^2}\]
\[5 = r\]

Answer 27

so now that you know the radius you can set up or write out the complete circle equation
and then you can try and graph that too, if you need to graph it as well
so how will the complete circle equation look like first?

Answer 28

(3+1)^2 + (0+3)^2 = 5

Answer 29

Me matey, that is not what we need .----.

Answer 30

this is the circle equation you need
\[(x+1)^2 + (y+3)^2 = 5^2 \]
or you can have 25 on the right side instead of the 5^2 either one is ok

Answer 31

so you leave the x and y in the equation?

Answer 32

Ye, the X and Y will remain as variables only the h, k and r are plugged in

Answer 33

alright, now do we draw the circle?

Answer 34

yes, now you can try and make up the graph for it, do you want to give it a try or do you want me to show you how the graph is done for that?

Answer 35

I did make one but I'm sure its not correct, do show

Answer 36

lol ok, first we can plot the center ... (I will do this one a sep page)
from the center we can use the radius of 5 to go up, left, right and down by 5 units and place a point at each new point...since we are given the point (3, 0) we can plot that one too ...and then we can try and connect those up into a circle shape as accurately as we can

and this is how the final piece looks like:
http://prntscr.com/6ruucz

Answer 37

ohhhhh

one more question, where is the radius line marked?

Answer 38

if you mean on the drawing, the radius was not drawn on the earlier drawing we had
usually the radius line is not really drawn... you use the radius value to get other useful points. You can connect the center to one of the points on the outside of the circle or even more of the points outside if you want to show one of the radii but technically there are an infinity of different radii for a circle so you can not really show all of them

Answer 39

ok makes sense, thanks Mira! xD you are beyond expert :D

Answer 40

Ahoy, me heartie! I am just a normal human being with a brain of Eisenstein (;

Answer 41

lol yeah that's a good one C;

Answer 42

:D