#80 Find the equation of the tangent plane to the hyperboloid

Find the equation of the tangent plane to the hyperboloid - Math

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Free Chegg Question

The equation of the tangent plane to the ellipsoid x²/a² + y²/b² + z²/c² = 1 at the point (x₀, y₀, z₀) can be written as

Find the equation of the tangent plane to the hyperboloid x²/a² + y²/b² - z²/c² = 1 at (x₀, y₀, z₀) and express it in a form similar to the one for the ellipsoid.

Free Chegg Answer

The equation of the tangent plane to the ellipsoid

at the point (x0,y0,z0) is

The equation of the tangent plane to the hyperboloid

at the point (x0,y0,z0) is
The difference between ellipsoid and hyperboloid is a sign of Z2 is negative.
So, the equation of the tangent hyperboloid is also similar to the tangent of the ellipsoid.
Change the sign of the coefficient of Z in

Hence, the equation of the tangent plane is