1. ## calculus- finding points

Consider the curve given by y^2 = 2 + xy.

It's derivative is y/(2y-x)

Find all points (x,y) on the curve where the line tangent to the curve has slope 1/2.

Thanks

2. Originally Posted by Mr_Green
Consider the curve given by y^2 = 2 + xy.

It's derivative is y/(2y-x)

Find all points (x,y) on the curve where the line tangent to the curve has slope 1/2.

Thanks
set the derivative = 1/2 and solve for the corresponding x's and y's

3. .5 = y / (2y-x)

how do i solve for this?

4. Originally Posted by Mr_Green
.5 = y / (2y-x)

how do i solve for this?
you can begin by multiplying both sides by (2y - x)

5. Originally Posted by Mr_Green
.5 = y / (2y-x)

how do i solve for this?
$\frac{1}{2} = \frac{y}{2y - x}$

$2y - x = 2y$

$x = 0$

So this is true for all points on the curve (0, y) such that $x \neq 2y$.

(You're in Calculus and you can't solve this???)

-Dan