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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
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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amistre64Best ResponseYou've already chosen the best response.1
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

amistre64Best ResponseYou've already chosen the best response.1
hmm, what methods have you been working with then? circles dont need calculus, but it does tend to be useful
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
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

samnathaBest ResponseYou've already chosen the best response.0
well this is under the geometry chapter
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
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

amistre64Best ResponseYou've already chosen the best response.1
the slope of the line itself is 5/b; which means that the slope would be 5/14 or smaller
 one year ago

samnathaBest ResponseYou've already chosen the best response.0
well the way we have been doing it is we get the radius and then use the distance formula ?
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
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

samnathaBest ResponseYou've already chosen the best response.0
is the radius not 13 ?
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
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

samnathaBest ResponseYou've already chosen the best response.0
ah its fine i did in the calculator haha
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
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

amistre64Best ResponseYou've already chosen the best response.1
y' = n/m for any point (n,.m) on the circle y = n/m (xn) + 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+5x12y%3D169
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
not the way your used to seeing it, but it was the only way that made sense to me :)
 one year ago

samnathaBest ResponseYou've already chosen the best response.0
ok it ok thanks well the answer in the back of the book is plus or minus 12
 one year ago

samnathaBest ResponseYou've already chosen the best response.0
so you are right anyway
 one year ago

amistre64Best ResponseYou've already chosen the best response.1
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

samnathaBest ResponseYou've already chosen the best response.0
haha thanks anyway its just my teacher she like to make thing complicated
 one year ago
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