Question

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?

Answer 1

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?

Answer 2

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.

Answer 3

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.

Answer 4

the second one would be x = 2, resulting in the original point (2,1), i think. but other than that, thank you sooooo much!

Answer 5

No.