Posted by **jane** on Friday, February 20, 2009 at 12:26am.

given the curve x + xy + 2y^2 = 6...

a. find an expression for the slope of the curve.

i got (-1-y)/(x + 4y) as my answer.

b. write an equation for the line tangent to the curve at the point (2,1).

i got y = (-1/3)x + (5/3).

but i didn't any answer for c!

c. find the coordinates of all other points on this curve with slopes equal to the the slope at (2,1).

do i just set (-1-y)/(x+4y) equal to -1/3?

- last calc question, i promise! -
**jane**, Friday, February 20, 2009 at 12:26am
i mean: do i just set (-1-y)/(x+4y) equal to -1/3 AND use the original formula to come up with an answer? like a two-variable system?

- last calc question, i promise! -
**jane**, Friday, February 20, 2009 at 12:29am
ALSO ALSO ALSO - on my first calc question (a couple posts down!), i added more to the problem that i forgot, so i need help with that too.

- last calc question, i promise! -
**Reiny**, Friday, February 20, 2009 at 12:41am
a) is correct

b) correct

c) yes, set (-1-y)/(x+4y) equal to -1/3

solving this I got x = 3-y

sub that back into the original equation to get after simplifying

y^2 + 2y - 3 = 0

(y+3)(y-1) = 0

y = -3 or y = 1

but those back into x=3-y for

x =6 or x = 4

so the other points are (6,-3) and (4,1)

you better check my math, it is getting late here.

- last calc question, i promise! -
**jane**, Friday, February 20, 2009 at 12:47am
the second one would be x = 2, resulting in the original point (2,1), i think. but other than that, thank you sooooo much!

- last calc question, i promise! -
**ncxnv**, Monday, September 29, 2014 at 7:43pm
No.

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