# Homework Help: Proof of x and y int of a line

1. Dec 11, 2009

### lax1113

1. The problem statement, all variables and given/known data
prove that $$\sqrt{x}$$ + $$\sqrt{y}$$ = c
Show that the sum of the x and y intercepts of any tangents to the line above = c (some positive constant).

2. Relevant equations
y1 - y2 = m(x1 - x2)
dy/dx(for this problem) = -$$\sqrt{y}$$/$$\sqrt{x}$$

3. The attempt at a solution
So I get the slope, as written above, and put it into a point/slope equation, but where from here? When I try to solve for y = 0 and x = 0 I always have y2 and x2 left, I think I might just be doing something completely wrong, I haven't done something like this for a while. Is this even the right direction? Solve for the y and x int by making the opposite 0 in the equation, and then try to get the results, (the two interecepts) to add up to be $$\sqrt{x}$$ + $$\sqrt{y}$$

2. Dec 11, 2009

### HallsofIvy

First problem, I don't know what "x1", "y1", "x2", and "y2" are since you don't say. You mean, I think, that the equation of the tangent line at $(x_1, y_1)$ is $y- y_1= m(x- x_1). But your real problem is that the derivative of y with respect to x is NOT [itex]-\sqrt{y}/\sqrt{x}$. You have x and y reversed.