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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

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    Ok. So to find the equation of a circle we need TWO things: the center of the circle and the radius

  3. anonymous
    • one year ago
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    okay how would we find those?

  4. anonymous
    • one year ago
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    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

  5. anonymous
    • one year ago
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    The mid-point formula is \[\left( \frac{ x _{2} + x _{1} }{ 2 }, \frac{ y _{2} + y _{1} }{ 2 } \right)\]

  6. anonymous
    • one year ago
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    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

  7. anonymous
    • one year ago
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    Try to plug in those x and y values into the formula, and then tell me what you got.

  8. anonymous
    • one year ago
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    \[\frac{ 18+2 }{ 2 },\frac{ 25+(-5) }{ 2 }\]okay so for the midpoint we would have this?

  9. anonymous
    • one year ago
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    which would be 10,10 right?

  10. anonymous
    • one year ago
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    @happyrosy sorry i had to leave

  11. anonymous
    • one year ago
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    okay so then the distance formula is \[\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}\]

  12. anonymous
    • one year ago
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    so then i plug them in which would be \[\sqrt{(18-2)^{2}+(25-(-5))^{2}}\]

  13. anonymous
    • one year ago
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    so that would lead to \[\sqrt{(16)^{2}+(30)^{2}}\]

  14. anonymous
    • one year ago
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    so we would then have \[\sqrt{256+900}\]

  15. anonymous
    • one year ago
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    so the square root of 1156 wich would be 34

  16. anonymous
    • one year ago
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    so 34 is the distance?

  17. anonymous
    • one year ago
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    (x-h)^2 + (y-k)^2 =r^2

  18. anonymous
    • one year ago
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    (x-10)^2 + (y-10)^2 = 1156

  19. anonymous
    • one year ago
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    okay i messed up with the radius but i think i got the distance right

  20. anonymous
    • one year ago
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    im going to go with (x − 10)2 + (y − 10)2 = 289

  21. anonymous
    • one year ago
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    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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