Let L be any tangent line to curve x^(0.5)+y^(0.5)=c^(0.5) (in the first quadrant). show that the sum of the x- and y- intercepts of L is c.?

Sol
x^(1/2)+y^(1/2)=c^(1/2)
(1/2)x^(－1/2)+(1/2)y^(－1/2)y’=0
x^(－1/2)+y^(－1/2)y’=0
y^(－1/2)y’=－x^(－1/2)
y’=－(x/y)^(－1/2)=－(y/x)^(1/2)
Set L：y－b=-(b/a)^(1/2)*(x－a)
a^(1/2)+b^(1/2)=c^(1/2)
When x=0
y－b=-(b/a)^(1/2)(－a)
y=b+(ab)^(1/2)
When y=0
0－b=－(b/a)^(1/2)*(x－a)
X－a=(ab)^(1/2)
x=a+(ab)^(1/2)
So
[b+(ab)^(1/2)]+[a+(ab)^(1/2)]
=a+b+2(ab)^(1/2)
=[a^(1/2)+b^(1/2)]^2
=[c^(1/2)]^2
=c