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Unofficialllyy

  • one year ago

Will fan and medal!!

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  1. Unofficialllyy
    • one year ago
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    Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit. x2 + 2x + y2 + 4y = 20

  2. Unofficialllyy
    • one year ago
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    \[x^2+2x+y^2+4y=20\]

  3. Unofficialllyy
    • one year ago
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    @welshfella

  4. Unofficialllyy
    • one year ago
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    I know I have to complete the square but I have no clue how to do it.

  5. welshfella
    • one year ago
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    convert it to the form (x - a)^2 + (y - b)^2 = r^2 complete the square x^2 + 2x and y^2 + 4y

  6. Unofficialllyy
    • one year ago
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    We use (h-k)^2+(y-k)^2=r^2 but it's the same thing as the form you gave me.

  7. welshfella
    • one year ago
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    x^2 + 2x + y^2 + 4y = 20 (x + 1)^2 - 1 + (y + 2)^2 - 4 = 20 to complete the square you take half of the coefficient of x then you have to subtract this value squared (x + 1)^2 = x^2 + 2x + 1 - so you have to subtract 1^2 from this to make x^2 + 2x

  8. welshfella
    • one year ago
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    (x + 1)^2 + (y + 2)^2 = 20+1 + 4 = 25 so if you compare this with the general equation you'll see that center = (-1,-2) and radius = sqrt25 = 5

  9. Unofficialllyy
    • one year ago
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    Thank you so much. I have one more question if you dont mind?

  10. welshfella
    • one year ago
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    well i must go in 10 minutes so we'll see how much i can do in that time

  11. Unofficialllyy
    • one year ago
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    Prove that the two circles shown below are similar.

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  12. Unofficialllyy
    • one year ago
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    I know that all circles are similar, but how do I prove it?

  13. welshfella
    • one year ago
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    oh must go now I'm sure jhannybean can help

  14. Unofficialllyy
    • one year ago
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    Okay thank you!

  15. Jhannybean
    • one year ago
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    \[x^2 + 2x + y^2 + 4y = 20\]\[(x^2+2x) + (y^2+4y)=20\]\[(x^2+2x+\color{red}{1}) +(y^2+4y+\color{red}{4})=20+\color{red}{1}+\color{red}{4}\]\[(x+1)^2+(y+2)^2=25~~~\checkmark \]

  16. Jhannybean
    • one year ago
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    Haha you dont have to @welshfella

  17. Unofficialllyy
    • one year ago
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    @Jhannybean Could you help with the circle question? It's my last one. :/

  18. Jhannybean
    • one year ago
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    hint: try creating triangles within the circles and then using their ratios in comparison.

  19. Jhannybean
    • one year ago
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    |dw:1440188772500:dw|

  20. Unofficialllyy
    • one year ago
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    So once i have the ratios what do i do?

  21. Jhannybean
    • one year ago
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    If we compare al the sides in a ratio, we would see it has a proportional relationship

  22. Jhannybean
    • one year ago
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    First find the hypotenuse of both triangles, the smaller triangle having a hypotenuse of x. and the bigger one having hypotenuse of y. \[c_1 : x^2= 2^2+2^2 = 8 \iff x=\sqrt{8}\]\[c_2 : y^2=5^2+5^2 = 50 \iff y=\sqrt{50}\]

  23. Unofficialllyy
    • one year ago
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    What about dilations? Couldn't we see if they are similar that way?

  24. Jhannybean
    • one year ago
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    Then we can say by the SSS theorem, \[\frac{2}{5} = \frac{\sqrt{8}}{\sqrt{50}}\]

  25. Jhannybean
    • one year ago
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    Hmm..i'm not really familiar with dilations! sorry.

  26. Unofficialllyy
    • one year ago
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    Okay well thank you!

  27. Jhannybean
    • one year ago
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    @cwrw238 could you help me understand dilations? :)

  28. Unofficialllyy
    • one year ago
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    I understand the way you did it, and it makes perfect sense, so no worries. :) thank you for your help!

  29. Jhannybean
    • one year ago
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    Oh cool! no problem.

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