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

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amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1well, the b is part of slope for the line, and a derivative is the slope of an equation .... can you do a derivative?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1hmm, what methods have you been working with then? circles dont need calculus, but it does tend to be useful

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1354822242160:dw im sure calculus would make it easier by far; are you in calculus and just learning derivatives by chance?

samnatha
 2 years ago
Best ResponseYou've already chosen the best response.0well this is under the geometry chapter

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1hmm 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
 2 years ago
Best ResponseYou've already chosen the best response.1the slope of the line itself is 5/b; which means that the slope would be 5/14 or smaller

samnatha
 2 years ago
Best ResponseYou've already chosen the best response.0well the way we have been doing it is we get the radius and then use the distance formula ?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1that 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

samnatha
 2 years ago
Best ResponseYou've already chosen the best response.0is the radius not 13 ?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1lol .... 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

samnatha
 2 years ago
Best ResponseYou've already chosen the best response.0ah its fine i did in the calculator haha

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1line 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?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1y' = 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

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1not the way your used to seeing it, but it was the only way that made sense to me :)

samnatha
 2 years ago
Best ResponseYou've already chosen the best response.0ok it ok thanks well the answer in the back of the book is plus or minus 12

samnatha
 2 years ago
Best ResponseYou've already chosen the best response.0so you are right anyway

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1yay!! ... 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

samnatha
 2 years ago
Best ResponseYou've already chosen the best response.0haha thanks anyway its just my teacher she like to make thing complicated
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