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anonymous
 one year ago
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
anonymous
 one year ago
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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok. So to find the equation of a circle we need TWO things: the center of the circle and the radius

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay how would we find those?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Since 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The midpoint formula is \[\left( \frac{ x _{2} + x _{1} }{ 2 }, \frac{ y _{2} + y _{1} }{ 2 } \right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Basically find the average of both x values and both y values from the coordinates given in order to determine the center of the circle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Try to plug in those x and y values into the formula, and then tell me what you got.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 18+2 }{ 2 },\frac{ 25+(5) }{ 2 }\]okay so for the midpoint we would have this?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which would be 10,10 right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@happyrosy sorry i had to leave

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so then the distance formula is \[\sqrt{(x2x1)^{2}+(y2y1)^{2}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so then i plug them in which would be \[\sqrt{(182)^{2}+(25(5))^{2}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so that would lead to \[\sqrt{(16)^{2}+(30)^{2}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so we would then have \[\sqrt{256+900}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the square root of 1156 wich would be 34

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so 34 is the distance?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(xh)^2 + (yk)^2 =r^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(x10)^2 + (y10)^2 = 1156

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay i messed up with the radius but i think i got the distance right

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im going to go with (x − 10)2 + (y − 10)2 = 289

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the 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!!
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