Question 1156589: Find the slope of the tangent at the point (0,2), the circle y^2+x^2=4
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the slope of the tangent at the point (0,2), the circle y^2+x^2=4
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The circle's center is the Origin.
(0,2) is a y-intercept ---> slope = 0
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The hard way:
y^2+x^2= 4
Differentiate implicitly.
2y*dy + 2x*dx = 0
dy/dx = -x/y --- (True for all circles centered at the Origin)
Slope = dy/dx = 0
Answer by ikleyn(52802)  (Show Source):
You can put this solution on YOUR website! .
The given point (0,2) is an endpoint of the vertical diameter.
The tangent line is horizontal at that point, and has, therefore, an equation
y = 2.
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