Question

Find an equation of the circle shown below.


(x + 10)2 + (y − 10)2 = 289
(x − 10)2 + (y − 10)2 = 289
(x − 10)2 + (y + 10)2 = 289
(x − 10)2 + (y − 10)2 = 17

Answer 1

Ok. So to find the equation of a circle we need TWO things: the center of the circle and the radius

Answer 2

okay how would we find those?

Answer 3

Since they did not give us the center, we have to use the midpoint formula. They also didn't give us the distance of the radius. We have to use the Distance formula. Ok so let's do this step by step

Answer 4

The mid-point formula is
\[\left( \frac{ x _{2} + x _{1} }{ 2 }, \frac{ y _{2} + y _{1} }{ 2 } \right)\]

Answer 5

Basically find the average of both x values and both y values from the coordinates given in order to determine the center of the circle

Answer 6

Try to plug in those x and y values into the formula, and then tell me what you got.

Answer 7

\[\frac{ 18+2 }{ 2 },\frac{ 25+(-5) }{ 2 }\]okay so for the midpoint we would have this?

Answer 8

which would be 10,10
right?

Answer 9

@happyrosy sorry i had to leave

Answer 10

okay so then the distance formula is \[\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}\]

Answer 11

so then i plug them in which would be \[\sqrt{(18-2)^{2}+(25-(-5))^{2}}\]

Answer 12

so that would lead to \[\sqrt{(16)^{2}+(30)^{2}}\]

Answer 13

so we would then have \[\sqrt{256+900}\]

Answer 14

so the square root of 1156 wich would be 34

Answer 15

so 34 is the distance?

Answer 16

(x-h)^2 + (y-k)^2 =r^2

Answer 17

(x-10)^2 + (y-10)^2 = 1156

Answer 18

okay i messed up with the radius but i think i got the distance right

Answer 19

im going to go with (x − 10)2 + (y − 10)2 = 289

Answer 20

the 34 you got was the diameter. Half of 34 is 17, which would be the radius. Square the 17, equaling to 289. So, yes your final is correct. GREAT JOB ON THE WORK!!