OpenStudy9
  • OpenStudy9
Need some Help with this coordinate geometry problem. Will medal+ fan!! Circle O has equation (x+2)^2 +(y-3)^2 =16. Circle K has equation (x-4)^2 + (y+1)^2=25. Relative to circle O and Circle K Where is point P(1,1)? A. Inside circle C and Outside Circle K B. Inside circle C and Circle K C. Outside circle C and Inside Circle K D. Outside circle C and Circle K E. At one of the intersections of Circle O and Circle K?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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whpalmer4
  • whpalmer4
Okay, here's where knowledge of the formulas will make your life much easier. \[(x-h)^2 + (y-k)^2 = r^2\]is the general formula for a circle with radius \(r\) and center at \((h,k)\) By comparing that with your formulas, you should be able to determine the radius and center of both circles. Make a sketch on a piece of paper and see where P(1,1) is in comparison to those two circles.
Michele_Laino
  • Michele_Laino
hint: center of circle O is \(O=(-2,3)\), whereas center of circle K is \(K=(4,-1)\), now please compute the subsequent distances: \(OP\), and \(KP\)
whpalmer4
  • whpalmer4
Distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) can be found with \[d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\]

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OpenStudy9
  • OpenStudy9
OK, one sec..
OpenStudy9
  • OpenStudy9
radius is 4 for the first one
OpenStudy9
  • OpenStudy9
and 5 for the next one
Michele_Laino
  • Michele_Laino
that's right!
OpenStudy9
  • OpenStudy9
So what is the next step?
whpalmer4
  • whpalmer4
But you may not need to actually calculate any distances here, just make the diagram (carefully) and look at it.
OpenStudy9
  • OpenStudy9
How do you draw the circles?
whpalmer4
  • whpalmer4
Do you have a drawing compass? Failing that, a ruler?
OpenStudy9
  • OpenStudy9
I have a ruler
whpalmer4
  • whpalmer4
Here's a graph of the two circles for you:
1 Attachment
OpenStudy9
  • OpenStudy9
It is B
OpenStudy9
  • OpenStudy9
Right? @whpalmer4
whpalmer4
  • whpalmer4
There's a website called https://www.geogebra.org that is useful for drawing these things, too. I don't use it myself, but many people here on OpenStudy do. Yes, B appears to be correct, assuming I drew the right circles :-)
OpenStudy9
  • OpenStudy9
Ok, thanks!

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