Proof of x and y int of a line

[lax1113]

Homework Statement

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).

Homework Equations

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

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}

 

[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). <br /> <br /> But your real problem is that the derivative of y with respect to x is NOT -\sqrt{y}/\sqrt{x}. You have x and y reversed.