anonymous
  • anonymous
Earthquakes release seismic waves that occur in concentric circles from the epicenter of the earthquake. Suppose a seismograph station determines the epicenter of an earthquake is located 9 kilometers from the station. If the epicenter is located at the origin, write the equation for the circular wave that passes through the station. A. x2 + y2 = 81 B. x2 + y2 = 9 C. (x - 9)2 + (y - 9)2 = 0 D. (x + 9)2 + (y + 9)2 = 0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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JamesJ
  • JamesJ
Which of these equations is the equation of circle of radius 9 centered at the origin?
JamesJ
  • JamesJ
Hint: the equation of a circle centered at \( (a,b) \) and of radius \( r \) is \[ (x-a)^2 + (y-b)^2 = r^2 \]
anonymous
  • anonymous
James <3 can you help me after by any chance?

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JamesJ
  • JamesJ
To make this as explicit as I can for you without giving the answer: if the circle is centered at the origin, then \[ (a,b) = (0,0) \] If the radius is 9 km, then \( r = 9 \). Now, using those values of the variables and the general form of the circle I wrote above, what is the equation of a circle, centered at the origin and of radius 9?
JamesJ
  • JamesJ
\[ (x-a)^2 - (y-b)^2 = r^2 \] Now fill in the values of the variables, \(a, b\) and \( r \).
JamesJ
  • JamesJ
**correction + \[ (x-a)^2 + (y-b)^2 = r^2 \]
anonymous
  • anonymous
Okay so, Take the epicentre as the centre point of the circle (Since earthquake waves are circular.) Then, since the epicentre is 9 km away, let the station be any point on the circle. So, radius= 9^2 = 81 So, equation of the circle: x^2 + y^2 = 81 is your answer.|dw:1328818229713:dw|
JamesJ
  • JamesJ
@vengance, why did you just give the answer? Wasn't it entirely obvious that I was helping the questioner get to the answer?
anonymous
  • anonymous
I think it's A. because it would be (x-o)^2 + (y-o)^2 = 9^2 , which equals 81.
JamesJ
  • JamesJ
yes, that's right.
anonymous
  • anonymous
@JamesJ= Why not? Some people understand via concepts as you are helping them, while others can learn better with examples which maybe used as reference questions.
anonymous
  • anonymous
It's okay James , i understand. Thank you for trying to help me without just giving me the answer. Although I do appreciate your answer too, vengeance921! Thank you both!! (:
anonymous
  • anonymous
Not a problem xD

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