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samnatha Group Title

find the values of b for which the line 5x + by = 169 is a tangent to x^2 + y^2 =169... please help

  • one year ago
  • one year ago

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  1. amistre64 Group Title
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    well, the b is part of slope for the line, and a derivative is the slope of an equation .... can you do a derivative?

    • one year ago
  2. samnatha Group Title
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    i don't think so

    • one year ago
  3. amistre64 Group Title
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    hmm, what methods have you been working with then? circles dont need calculus, but it does tend to be useful

    • one year ago
  4. amistre64 Group Title
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    |dw:1354822242160:dw| im sure calculus would make it easier by far; are you in calculus and just learning derivatives by chance?

    • one year ago
  5. samnatha Group Title
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    well this is under the geometry chapter

    • one year ago
  6. amistre64 Group Title
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    hmm well, the y intercept of the line would need to be greater that 14 to at least have shot at being tangent to the circle 169/b > 14; 169/14 > b ... 14 > b

    • one year ago
  7. amistre64 Group Title
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    the slope of the line itself is -5/b; which means that the slope would be -5/14 or smaller

    • one year ago
  8. samnatha Group Title
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    well the way we have been doing it is we get the radius and then use the distance formula ?

    • one year ago
  9. amistre64 Group Title
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    that does sound like something more doable to me :) radius is sqrt(169) = 14 and the slope of the radius would have to be b/5 to be perp to the line

    • one year ago
  10. samnatha Group Title
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    is the radius not 13 ?

    • one year ago
  11. amistre64 Group Title
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    lol .... fine, if you wanna be "correct" and all. 12: 144 13: 169 yeah it is ... i tend to get it mixed around with the 14 14: 196

    • one year ago
  12. samnatha Group Title
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    ah its fine i did in the calculator haha

    • one year ago
  13. amistre64 Group Title
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    line of the radius would have to be: y = b/5 x line of the tangent is given as: y = -5/b x + 169/b any way to compare the 2?

    • one year ago
  14. samnatha Group Title
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    divide by b ?

    • one year ago
  15. amistre64 Group Title
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    y' = -n/m for any point (n,.m) on the circle y = -n/m (x-n) + m would be the tangent line of the circle and this has to equal the given line, with the same point (n.m) 5n +bm = 169 \[y = -\frac{n}{m}x+\frac{n^2+m^2}{m} \] 5n +bm = 169 comparing intercepts; i would say that 5^2+b^2 = 169 b^2 = 144 b = -12 , 12 lets see if the wolf likes it :) http://www.wolframalpha.com/input/?i=x%5E2%2By%5E2%3D169%2C+5x%2B12y%3D169%2C+5x-12y%3D169

    • one year ago
  16. amistre64 Group Title
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    not the way your used to seeing it, but it was the only way that made sense to me :)

    • one year ago
  17. samnatha Group Title
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    ok it ok thanks well the answer in the back of the book is plus or minus 12

    • one year ago
  18. samnatha Group Title
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    so you are right anyway

    • one year ago
  19. amistre64 Group Title
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    yay!! ... i got no idea how id try to approach it using the distance and radius stuff. Either too long out of geometry or never really learnt it to begin with

    • one year ago
  20. samnatha Group Title
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    haha thanks anyway its just my teacher she like to make thing complicated

    • one year ago
  21. amistre64 Group Title
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    good luck ;)

    • one year ago
  22. samnatha Group Title
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    thanks

    • one year ago
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