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odehye

  • 2 years ago

Graph X^2 + (y +3)^2=9

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  1. AccessDenied
    • 2 years ago
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    Are you familiar with what sort of shape you'll get from an equation of this form?

  2. odehye
    • 2 years ago
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    Not this one

  3. AccessDenied
    • 2 years ago
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    Okay. Equations of the form \((x - h)^2 + (y - k )^2 = r^2\) are considered circles. The center of the circle is (h, k), and the radius is r. So, you can usually make comparisons between the 'standard form'and the given equation to figure out your center + radius, and graph from that. :)

  4. odehye
    • 2 years ago
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    will the center b (0,-3)?

  5. AccessDenied
    • 2 years ago
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    Yes, that is correct.

  6. odehye
    • 2 years ago
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    So then this will be a circle intersecting at ±3 all round

  7. AccessDenied
    • 2 years ago
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    Hmm... well, the circle simply has a radius of three, so basically all the points that are a distance of 3 from (0, -3) are points on your graph. It makes sense if you consider r the distance between the center and all the points on the circle that are 3 units away. :)

  8. odehye
    • 2 years ago
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    |dw:1352106893652:dw|

  9. AccessDenied
    • 2 years ago
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    The exact center of the circle will be at (0, -3), like this: |dw:1352107269477:dw|

  10. odehye
    • 2 years ago
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    Since the radius is 9 and the √9=3

  11. AccessDenied
    • 2 years ago
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    Our radius is determined as r^2 = 9 => r = 3. :) So, we can draw in all the points around (0, -3) that are a distance of 3 units away for the circle.

  12. AccessDenied
    • 2 years ago
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    |dw:1352107502707:dw| So, we can pick out a few simple ones that line up on the axes, and then we have to estimate from there. My graph isn't drawn particularly well, so it doesn't look very nice, but you should be able to get a circle. :P

  13. odehye
    • 2 years ago
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    So the points are (0,0) (3,-3) (0,-6) (-3,-3)?

  14. AccessDenied
    • 2 years ago
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    Yes, those are a few points on the graph of the circle. If you start from your center, it is easiest to move horizontally or vertically by the same distance as the radius to find four points to draw the rest of the graph from.

  15. AccessDenied
    • 2 years ago
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    The process of graphing the circle basically goes like this: 1) Find your center-point and radius 2) Plot the center-point on your graph 3) Plot those four points at a distance of one radius away and draw in the circle from there as best you can. Usually teachers will be forgiving as long as you have those four points marked and your circle looks somewhere close. :P

  16. odehye
    • 2 years ago
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    You've been so much helpful

  17. odehye
    • 2 years ago
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    I have about 6 more qtns to go. I'm staying awake till class time which is 7am

  18. AccessDenied
    • 2 years ago
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    I'm glad to be able to help! :) Although, I will have to get off. I should really be sleeping...

  19. odehye
    • 2 years ago
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    Sure. Thank a million.

  20. odehye
    • 2 years ago
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    Good night and sound sleep.

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