Intercept of ellipse & implicit differ.

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Help,
I'm too stoopid to do my homework.

What is: If x^1/2+y^1/2=3, what is the value of dx/dy at the point (4,1)?
What is: The y-intercept of the tangent line to the ellipse x^2+3y^2=1 at the point (1/2, 1/2)?

Are these easy questions? Sad

There are also slope fo the tangent to the curve questions:

What is: The slope of the tangent to the curve xy^2+x^2y=2 at the point (1,1)?

Where do I start?! Evil or Very Mad

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Take the derivative and separate variables

x^(1/2)+y^(1/2)=3
(1/2)x^(-1/2)dx+(1/2)y^(-1/2)dy=0
x^(-1/2)dx+y^(-1/2)dy=0
dy/dx=m=-(y/x)^(1/2)
@ (1,4)
dy/dx=-(4/1)^(1/2)=-2
so m of tangent line = -2
put this into the slope intercept form of a line, plug in (1,4) and determine b (y intercept)

Do the same thing to x^2+3y^2=1 @ (1/2, 1/2) & xy^2+x^2y=2 @ (1,1)

Rap

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Intercept of ellipse & implicit differ.

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