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

Question

asked May 14, 2024 201k views

1 Answer

Imbryk · Answer 1 · 2024-05-18T23:57:28+0000

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