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

- anonymous

- schrodinger

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- shubhamsrg

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

- anonymous

whats the dy/dx ?

- shubhamsrg

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

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

- shubhamsrg

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

- anonymous

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

- shubhamsrg

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

- anonymous

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

- RadEn

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

- anonymous

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

- RadEn

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 ?

- anonymous

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

- RadEn

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

- anonymous

is it 3 ?

- RadEn

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

- anonymous

so the slope would be -3/4 ?

- RadEn

looks too many formula above, hahaha...

- anonymous

haha is it right ?

- RadEn

yes, of couse

- anonymous

oh thank god haha

- RadEn

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

- anonymous

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

- RadEn

what's the book answer ?

- anonymous

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

- RadEn

wait, i will check it...

- anonymous

ok thanks :)

- RadEn

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

- anonymous

i have no idea where i went wrong ?

- RadEn

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

- RadEn

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

- anonymous

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

- RadEn

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

- anonymous

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

- RadEn

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

- anonymous

whats *sqrt ? is it square root?

- RadEn

* the symbol of multiplication
sqrt = square root

- anonymous

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

- RadEn

hahahaha... u must KNOW it

- anonymous

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

- RadEn

you're welcome :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.