Question

find the tangent line to x^2 + 2y = 8 and parallel to 2x - y = 4

Answer 1

need to use calculus

Answer 2

just give me the steps and i'll try solving for it.. thanks

Answer 3

find the derivative of the curve, that will give you an equation for the slope at any point on the curve.

find the slope of the line 2x - y - 4
use that slope in the first equation

Answer 4

will i equate the curve to y first? then defferentiate it?

Answer 5

yes, solve for y (because you want to find dy/dx = slope)

or you can use implicit differentiation if you know how.

Answer 6

i arrive at two different answers..
1st what i did is 2y = 8 - x^2 .. then i devide 2.. so what i got is y = (8 - x^2)/2 .. derive.. i got dy/dx = -x.
then i tried doing implicit
i got dy/dx = -2x

so which is correct?

Answer 7

implict:
x^2 + 2y = 8
2 x dx/dx + 2 dy/dx = 0
2x + 2 dy/dx =0
x + dy/dx =0
dy/dx = -x

Answer 8

owh.. yes.. sorry.. got confused

Answer 9

Here is a plot

Answer 10

what is the purpose of dy/dx = -x ?

Answer 11

that is the slope of the curve (as a function of x)
at x=0 the slope is -0 = 0

you want to find the x on the curve where the slope matches the line they gave you

Answer 12

ok.. then solve for the slope of 2x - y - 4 = 0.. i got 2.. what next?

Answer 13

find the tangent line to x^2 + 2y = 8
where on the curve x^2 +2y =8 does it have a slope of 2 ?

Answer 14

got confused @.@

Answer 15

when you get a chance, watch this
http://www.khanacademy.org/math/calculus/differential-calculus/derivative_intro/v/calculus--derivatives-1--new-hd-version

meanwhile, dy/dx = -x (the derivative of x^2 + 2y=8 ) tells you the slope of the tangent line of that curve at any point x

Answer 16

you want the tangent line that has a slope of 2 (to match the slope of the line 2x - y = 4)

m= -x
2 = -x
so x= -2

at x=-2 the tangent line to the curve will have a slope of 2 (see post up above of the plot)

Answer 17

now you need to find the y value on the curve when x= -2

that will give you a point on the curve (-2, ?)
you have the slope m=2
now you can write down the equation of the line through that point with slope =2

Answer 18

where will i substitute the value -2?

Answer 19

if you want the (x,y) values of a point on the curve, and you have x= -2, how do you find y ?

Answer 20

substitute -2 from x.. 2^2 + 2y = 8 ... 2y = 4 .. y = 2.. is that correct?

Answer 21

yes

Answer 22

then i will just need to use point-slope formula to find the equation of the line perpendicular to 2x - y - 4 = 0 ?

Answer 23

though you should write it as (-2)^2 + 2y = 8

Answer 24

find the tangent line to x^2 + 2y = 8 and *parallel* to 2x - y = 4

Answer 25

the tangent line will have the pass the point (-2,4) ?

Answer 26

? I thought you found y=2 at x=-2

Answer 27

yes.. sorry.. got wrong with my typing.. (-2,2)
so
y-y1=m(x-x1)
y - 2 = 2(x+2)
y = 2x + 6.. that is the equation of the tanget line

Answer 28

looks good

Answer 29

is that correct?? so that is perpendicular to 2x-y-4 because they have the same slope..

Answer 30

you mean parallel

perpendicular means they form a right angle (and the slopes are negative reciprocals)

Answer 31

ahh yes.. but is my answer correct already? so i can ask some questions again

Answer 32

yes you found the tangent line that is parallel to the given line

Answer 33

thanks ! you're a great help, and a good tutor..