## samnatha 2 years ago 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

1. shubhamsrg

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

2. samnatha

whats the dy/dx ?

3. shubhamsrg

i see..why are you studying tangents then ? you need to clear up the basics first..

4. samnatha

am well my teacher probably does it a different way than you do...

5. shubhamsrg

hmm..what does he do? differentiate instead of finding dy/dx? o.O

6. samnatha

no we have never done differentiate yet just what does dy/ dx stand for ?

7. shubhamsrg

it'll come after you differentiate,,nevermind,,must be some alternative way then..

8. samnatha

like usually we would just sub one of the equations in but i tried doin it like that and it just looks complicated

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

10. samnatha

ok that seems more familiar we use the formula y - y1 = m(x-x1)

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 ?

12. samnatha

(3,1) is the center and the radius is 5

yes.. correct next can u determine the slope of line which parallel with line 3x + 4y + 10 = 0 ?

14. samnatha

is it 3 ?

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

16. samnatha

so the slope would be -3/4 ?

looks too many formula above, hahaha...

18. samnatha

haha is it right ?

yes, of couse

20. samnatha

oh thank god haha

u just plug of them, write out ur equation welcome...

22. samnatha

the answer in the back of the book id diff from the answer i got

24. samnatha

3x + 4y + 12 =0 or 3x + 4y - 38 = 0

wait, i will check it...

26. samnatha

ok thanks :)

the formula above have worked... i got like ur book answer

28. samnatha

i have no idea where i went wrong ?

ok, let's check it steps by steps...

first, we have the center of circle (3,1) and its radius = 5 right ?

31. samnatha

oh wait i know what i did i didn't use the whole formula only the first part

then the sope of line 3x+4y+10=0 is m1=-3/4 so, m2 = -3/4 also (because parallel)

33. samnatha

i got so far 3x+4y - 13 = +- 25(25/16) ?

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

35. samnatha

whats *sqrt ? is it square root?

* the symbol of multiplication sqrt = square root

37. samnatha

oooh thats what i was doing rong i didn't know what that was :P

hahahaha... u must KNOW it

39. samnatha

haha sorry yeah i got it now i was squaring 5 :P whoops thanks for your help

you're welcome :)

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