Question

Equation of a line tangent to the curve xy = √(xy – x) + 1 at the point (1, 2)? I have some work done...

Answer 1

So I did manage to differentiate it: (x(3-2xy))/(1-3y+2xy^2), and then I plugged in my values for x and y, (1,2) and got -1/3. Am I on track so far? What would the equation of the tangent lint be then?

Answer 2

*line

Answer 3

well if you have the slope (m)...then equation of tangent line is:
y - y1 = m(x -x1)
x1,y1 is point line goes through (1,2)

y-2 = -1/3(x-1)

Answer 4

That's my problem at this point. When I isolate y, I get (7-x)/3, which is not equivalent to any of my answer choices.

Answer 5

what did you get when you differentiate ?

Answer 6

(x(3-2xy))/(1-3y+2xy^2) Did I do something wrong differentiating? (I'm not that great with implicit stuff, so that might be the case.)

Answer 7

yes, sorry i didn't check before....your derivative is wrong
when you have to do implicit differentiation, don't forget to use product rule
\[(xy)' = xy' + x'y = x \frac{dy}{dx} + y\]

Answer 8

\[\rightarrow x \frac{dy}{dx} +y = \frac{x \frac{dy}{dx} +y -1}{2 \sqrt{xy-x}}\]

Answer 9

\[\rightarrow \frac{dy}{dx} = \frac{-2y \sqrt{xy-x} +y-1}{x(2 \sqrt{xy-x} -1)}\]

Answer 10

were you able to follow my work? got the answer now

Answer 11

Yes I think so -- plug and chug: (-2(2)sqrt(1(2)-1)+(2)-1)/(1(2sqrt(1(2)-1)-1)) = 3 is what I got. Plugging that in and solving for y gives me 3x-1, but that's still not in the answer choices... It's close to option A. I might just go with that.

Answer 12

haha yes that would be a good educated guess.
that is the answer...slope should come out to be -3 when you plug in (1,2)

Answer 13

Oh durr, it's -3, and that changes everything
It's A, thank you for putting me on track with the differentiation!

Answer 14

no problem