anonymous
  • anonymous
find the values of b for which the line 5x + by = 169 is a tangent to x^2 + y^2 =169... please help
Mathematics
jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
well, the b is part of slope for the line, and a derivative is the slope of an equation .... can you do a derivative?
anonymous
  • anonymous
i don't think so
amistre64
  • amistre64
hmm, what methods have you been working with then? circles dont need calculus, but it does tend to be useful

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amistre64
  • amistre64
|dw:1354822242160:dw| im sure calculus would make it easier by far; are you in calculus and just learning derivatives by chance?
anonymous
  • anonymous
well this is under the geometry chapter
amistre64
  • amistre64
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
amistre64
  • amistre64
the slope of the line itself is -5/b; which means that the slope would be -5/14 or smaller
anonymous
  • anonymous
well the way we have been doing it is we get the radius and then use the distance formula ?
amistre64
  • amistre64
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
anonymous
  • anonymous
is the radius not 13 ?
amistre64
  • amistre64
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
anonymous
  • anonymous
ah its fine i did in the calculator haha
amistre64
  • amistre64
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?
anonymous
  • anonymous
divide by b ?
amistre64
  • amistre64
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
amistre64
  • amistre64
not the way your used to seeing it, but it was the only way that made sense to me :)
anonymous
  • anonymous
ok it ok thanks well the answer in the back of the book is plus or minus 12
anonymous
  • anonymous
so you are right anyway
amistre64
  • amistre64
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
anonymous
  • anonymous
haha thanks anyway its just my teacher she like to make thing complicated
amistre64
  • amistre64
good luck ;)
anonymous
  • anonymous
thanks

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