Ask your own question, for FREE!
Mathematics 48 Online
OpenStudy (anonymous):

Given:f(x,y) = x^2 + 4y^2...Find an equation for the tangent line to the curve which its intersection of the surface z=(x,y) and the plane y=1 through the point (-1,1,5)

OpenStudy (amistre64):

so when y=1 z = x^2 +4(1)

OpenStudy (amistre64):

z' = 2x ; (-1,5) tanz = 2(-1)x -2(-1)(-1) + 5

OpenStudy (anonymous):

Im confused so whats the Eq. of the tangent line??

OpenStudy (amistre64):

if your confused, then what you need is clarification on the process, and not just the results ...

OpenStudy (anonymous):

I know amistre I just dont have the book in front of me since im at work, I will look over when i get home, thanks again!!

OpenStudy (amistre64):

we determine the equation for f(x,y) when y=1 as stated in the problem z = x^2 + 4 is the outcome right?

OpenStudy (anonymous):

yes no doubting that

OpenStudy (amistre64):

then the derivative of z at this equation gives us the slope along any point ... z' = 2x correct?

OpenStudy (anonymous):

yes so thats the equation i would think. but i saw you do some thing with tan?

OpenStudy (amistre64):

the equation for the tangent uses this for slope; and is anchored to the intended point

OpenStudy (amistre64):

since x=-1; the slope of the line is 2(-1) = -2

OpenStudy (amistre64):

tanz = mx -mPx + Py givent that (Px,Py) is (-1,5) tanz = -2x +2(-1) + 5 tanz = -2x +3 but im not sure if they want that in parametric form or not

OpenStudy (anonymous):

Ohh I see. I am not sure doesnt say. how would i make parametric

OpenStudy (anonymous):

Also, would i do inverse tangent for solve for z? or do we genrally leave the equation of a tangent line in this type ofr form (tanz=-2x+3)

OpenStudy (amistre64):

x is independant so x =0+1t y = 1 so y=1 + 0t z depends on x = -2x+3 -> 2 -2t

OpenStudy (amistre64):

tanz is just my notation to indicate that this is a tangent line using z as the dependant variable

OpenStudy (amistre64):

and if we claen up the tyops .... or at least the ones that were made previously lol x = 0 + t y = 1+0t z = 3 -2t

OpenStudy (anonymous):

cool thanks a bunch

OpenStudy (amistre64):

yw

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
Unknownuser8009: What desserts would be the easiest to make (based on experience)?
22 minutes ago 23 Replies 2 Medals
vile: any bleach fans?
2 hours ago 5 Replies 1 Medal
H1m: bro. I have couple questions..
7 hours ago 2 Replies 1 Medal
H1m: how do I know if I have SUB?
2 hours ago 4 Replies 0 Medals
Gucchi: programming help
10 hours ago 9 Replies 1 Medal
AddieroniAndCheese: Call me egotistical, and that i can't deny Cuz im hittinu2019 it spittin it Busti
2 hours ago 10 Replies 3 Medals
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!