Question

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

Answer 1

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

Answer 2

whats the dy/dx ?

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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 ?

Answer 12

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

Answer 13

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

Answer 14

is it 3 ?

Answer 15

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

Answer 16

so the slope would be -3/4 ?

Answer 17

looks too many formula above, hahaha...

Answer 18

haha is it right ?

Answer 19

yes, of couse

Answer 20

oh thank god haha

Answer 21

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

Answer 22

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

Answer 23

what's the book answer ?

Answer 24

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

Answer 25

wait, i will check it...

Answer 26

ok thanks :)

Answer 27

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

Answer 28

i have no idea where i went wrong ?

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

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

Answer 35

whats *sqrt ? is it square root?

Answer 36

* the symbol of multiplication
sqrt = square root

Answer 37

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

Answer 38

hahahaha... u must KNOW it

Answer 39

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

Answer 40

you're welcome :)