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Find the equation of the tangent through the point (2,-2) to the hyperbola x² + y² = 16​

User Savage
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1 Answer

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Answer: y = -x

Explanation:

The equation of the hyperbola is x² - y² = 16.

Taking the derivative of the equation with respect to x, we get:

2x - 2yy' = 0

y' = x / y

At the point (2,-2), we have x = 2 and y = -2. Thus, the slope of the tangent is:

y' = 2 / (-2) = -1

So, the equation of the tangent through the point (2,-2) is:

y + 2 = -1(x - 2)

y + 2 = -x + 2

y = -x

User Imbryk
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8.5k points
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