[" Ui) "x" a "y^(2)" and "y=2a" when "x=a],[" show that "y^(2)=lg x" ."]

x prop y^2 and y = 2a when x = a, then show that y^2 = 4ax .

If x/y alphax+y and y/x alpha x-y , then show that x^2-y^2 = constant.

if y=sqrt(x^(2)+a^(2)), then show that y(dy)/(dx)=x

If log (x^(2)+y^(2)) = 2 tan ^(-1) (x/y) " then show that " (dy)/(dx) = (y-x)/(y +x)

If log (x^(2)+y^(2)) = 2 tan ^(-1) (x/y) " then show that " (dy)/(dx) = (y-x)/(y +x)

IF [log (x^2 + y^2) = 2 tan^-1 (y/x)] then show that , dy/dx = (x+y) /(x- y)

2 x y+y^2-2 x^2 (dy)/(dx)=0 , y=2 when x=1

If the points (x_1, y_1), (x_2, y_2) and (x_3, y_3) be collinear, show that: (y_2 - y_3)/(x_2 x_3) + (y_3 - y_1)/(x_3 x_2) + (y_1 - y_2)/(x_1 x_2) = 0

If (u^2+v^2) prop (x^2 +y^2 ) and uv prop xy then show that (u+v) prop (x+y) when u/v+v/u=x/y +y/x .

"If "log(x^(2)+y^(2))=2tan^(-1)""((y)/(x))," show that "(dy)/(dx)=(x+y)/(x-y)