anonymous
  • 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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
anonymous
  • anonymous
Ok. So to find the equation of a circle we need TWO things: the center of the circle and the radius
anonymous
  • anonymous
okay how would we find those?

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anonymous
  • 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
anonymous
  • anonymous
The mid-point formula is \[\left( \frac{ x _{2} + x _{1} }{ 2 }, \frac{ y _{2} + y _{1} }{ 2 } \right)\]
anonymous
  • 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
anonymous
  • anonymous
Try to plug in those x and y values into the formula, and then tell me what you got.
anonymous
  • anonymous
\[\frac{ 18+2 }{ 2 },\frac{ 25+(-5) }{ 2 }\]okay so for the midpoint we would have this?
anonymous
  • anonymous
which would be 10,10 right?
anonymous
  • anonymous
@happyrosy sorry i had to leave
anonymous
  • anonymous
okay so then the distance formula is \[\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}\]
anonymous
  • anonymous
so then i plug them in which would be \[\sqrt{(18-2)^{2}+(25-(-5))^{2}}\]
anonymous
  • anonymous
so that would lead to \[\sqrt{(16)^{2}+(30)^{2}}\]
anonymous
  • anonymous
so we would then have \[\sqrt{256+900}\]
anonymous
  • anonymous
so the square root of 1156 wich would be 34
anonymous
  • anonymous
so 34 is the distance?
anonymous
  • anonymous
(x-h)^2 + (y-k)^2 =r^2
anonymous
  • anonymous
(x-10)^2 + (y-10)^2 = 1156
anonymous
  • anonymous
okay i messed up with the radius but i think i got the distance right
anonymous
  • anonymous
im going to go with (x − 10)2 + (y − 10)2 = 289
anonymous
  • 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!!

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