OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):
2 years ago

OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

okay how would we find those?

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

which would be 10,10 right?

2 years ago
OpenStudy (anonymous):

@happyrosy sorry i had to leave

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

so the square root of 1156 wich would be 34

2 years ago
OpenStudy (anonymous):

so 34 is the distance?

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

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!!

2 years ago