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samnatha

help me please Find the equation of the tangents to the circle x^2 + y^2 - 6x - 2y - 15 = 0 which are parallel to the line 3x + 4y + 10 = 0

  • one year ago
  • one year ago

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  1. shubhamsrg
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    find dy/dx of the circle and the line.. equate both since both are parallel and thus find out the eqn..

    • one year ago
  2. samnatha
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    whats the dy/dx ?

    • one year ago
  3. shubhamsrg
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    i see..why are you studying tangents then ? you need to clear up the basics first..

    • one year ago
  4. samnatha
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    am well my teacher probably does it a different way than you do...

    • one year ago
  5. shubhamsrg
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    hmm..what does he do? differentiate instead of finding dy/dx? o.O

    • one year ago
  6. samnatha
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    no we have never done differentiate yet just what does dy/ dx stand for ?

    • one year ago
  7. shubhamsrg
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    it'll come after you differentiate,,nevermind,,must be some alternative way then..

    • one year ago
  8. samnatha
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    like usually we would just sub one of the equations in but i tried doin it like that and it just looks complicated

    • one year ago
  9. RadEn
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    hmmm.. i think he not yet learned about differentiate so, for basic u can use the formula : y - b = m(x-a) + - r*sqrt(m^2+1) with a,b is the center of circle, m slope and r radius therefore, first u have to determines all components above

    • one year ago
  10. samnatha
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    ok that seems more familiar we use the formula y - y1 = m(x-x1)

    • one year ago
  11. RadEn
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    that is the equation of the tangents to the circle sign +- means there are 2 equations there so, if given equation of circle : x^2 + y^2 - 6x - 2y - 15 = 0 what;s the center of circle and it radius ?

    • one year ago
  12. samnatha
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    (3,1) is the center and the radius is 5

    • one year ago
  13. RadEn
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    yes.. correct next can u determine the slope of line which parallel with line 3x + 4y + 10 = 0 ?

    • one year ago
  14. samnatha
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    is it 3 ?

    • one year ago
  15. RadEn
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    use the property : m1 = m2 (because the lines are parallel) hint : if given a straight line ax+by+c=0, to find slope u can use the formula m=-a/b

    • one year ago
  16. samnatha
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    so the slope would be -3/4 ?

    • one year ago
  17. RadEn
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    looks too many formula above, hahaha...

    • one year ago
  18. samnatha
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    haha is it right ?

    • one year ago
  19. RadEn
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    yes, of couse

    • one year ago
  20. samnatha
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    oh thank god haha

    • one year ago
  21. RadEn
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    u just plug of them, write out ur equation welcome...

    • one year ago
  22. samnatha
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    the answer in the back of the book id diff from the answer i got

    • one year ago
  23. RadEn
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    what's the book answer ?

    • one year ago
  24. samnatha
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    3x + 4y + 12 =0 or 3x + 4y - 38 = 0

    • one year ago
  25. RadEn
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    wait, i will check it...

    • one year ago
  26. samnatha
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    ok thanks :)

    • one year ago
  27. RadEn
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    the formula above have worked... i got like ur book answer

    • one year ago
  28. samnatha
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    i have no idea where i went wrong ?

    • one year ago
  29. RadEn
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    ok, let's check it steps by steps...

    • one year ago
  30. RadEn
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    first, we have the center of circle (3,1) and its radius = 5 right ?

    • one year ago
  31. samnatha
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    oh wait i know what i did i didn't use the whole formula only the first part

    • one year ago
  32. RadEn
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    then the sope of line 3x+4y+10=0 is m1=-3/4 so, m2 = -3/4 also (because parallel)

    • one year ago
  33. samnatha
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    i got so far 3x+4y - 13 = +- 25(25/16) ?

    • one year ago
  34. RadEn
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    now, aplly of them to the formula : y - b = m(x-a) + - r*sqrt(m^2+1) y-1 = -3/4(x-3) + - 5 * sqrt((-3/4)^2 + 1) y-1 = -3/4(x-3) + - 5 * sqrt(25/16) y-1 = -3/4(x-3) + - 5 * 5/4 y-1 = -3/4(x-3) + - 25/4 multiply by 4 to both sides, gives 4(y-1) = -3(x-3) +- 25 4y - 4 = -3x + 9 +- 25 3x + 4y - 4 -9 +- 25 = 0 3x + 4y - 13 + - 25 = 0 the first equation : 3x + 4y - 13 + 25 = 0 3x + 4y + 12 = 0 2nd equation : 3x + 4y - 13 - 25 = 0 3x + 4y - 38 = 0

    • one year ago
  35. samnatha
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    whats *sqrt ? is it square root?

    • one year ago
  36. RadEn
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    * the symbol of multiplication sqrt = square root

    • one year ago
  37. samnatha
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    oooh thats what i was doing rong i didn't know what that was :P

    • one year ago
  38. RadEn
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    hahahaha... u must KNOW it

    • one year ago
  39. samnatha
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    haha sorry yeah i got it now i was squaring 5 :P whoops thanks for your help

    • one year ago
  40. RadEn
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    you're welcome :)

    • one year ago
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