Question

The equation of curve is sqrt(x)+sqrt(y)=sqrt(a)
where is a positive constant. express dy/dx in terms of x and y
the straight line with equation y=x intersects the curve at the point P. Find the equation of the tangent to the curve at P.

Answer 1

\[1/2\sqrt{x}+dy/dx(1/2\sqrt{y}=0\]\[dy/dx=1/2\sqrt{x}*2\sqrt{y}/1\]\[\sqrt{y}/\sqrt{x}=dy/dx\]