## 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

1. 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?

2. samnatha

i don't think so

3. amistre64

hmm, what methods have you been working with then? circles dont need calculus, but it does tend to be useful

4. amistre64

|dw:1354822242160:dw| im sure calculus would make it easier by far; are you in calculus and just learning derivatives by chance?

5. samnatha

well this is under the geometry chapter

6. 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

7. amistre64

the slope of the line itself is -5/b; which means that the slope would be -5/14 or smaller

8. samnatha

well the way we have been doing it is we get the radius and then use the distance formula ?

9. 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

10. samnatha

is the radius not 13 ?

11. 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

12. samnatha

ah its fine i did in the calculator haha

13. 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?

14. samnatha

divide by b ?

15. 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

16. amistre64

not the way your used to seeing it, but it was the only way that made sense to me :)

17. samnatha

ok it ok thanks well the answer in the back of the book is plus or minus 12

18. samnatha

so you are right anyway

19. 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

20. samnatha

haha thanks anyway its just my teacher she like to make thing complicated

21. amistre64

good luck ;)

22. samnatha

thanks