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Home Q & A Board Science-Related Homework Help Mathematics
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irina irina
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12 years ago
Please help Frowning Face I honestly never learned this in class and I have a test soon! The question is : Find the equation of the tangent line to the graph of x^2(multiply by)y^2=1 at the point (4, 1/2) and at the point (4,-1/2)
Thank you!
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nywoodsnywoods
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#1
12 years ago
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#2
12 years ago
I can tell you how to find the equation of the tangent line.

To find the equation of the tangent line, you will have to take the derivative of the original function.
(x^2)(y^2) = 1
solve for y and you get:
y = 1/x
Now you take the derivative by first reorganizing the equation
y = x^-1
y = -x^-2
y = -1/x^2

So the equation of the tangent line will be: y = -1 / x^2
So at (4,0.5) the slope is -1/16 and the slope at (4,-0.5) is the same.

so the equation will become:
 y-y1=m(x2-x1)

y-0.5 = (-1/16)(x-4) at point (4,1/2)
or
y+0.5 = (-1/16)(x-4) at point (4,-1/2)
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