Question

The equation of the tangent plane to the ellipsoid x^2/a^2 + y^2/b^2 + z^2/c^2 = 1 at the point (x0, y0, z0) can be written as xx0/a^2 + yy0/b^2 + zz0/c^2 = 1 Find the equation of the tangent plane to the hyperboloid x^2/a^2 + y^2/b^2 - z^2/c^2 = 1 at (x0, y0, z0) and express it in a form similar to the one for the ellipsoid.

Name: the equation of the tangent plane to the ellipsoid x2a2 y2b2 z2c2 1 at the point x0 y0 z0 can be written as xx0 a2 yy0 b2 zz0 c2 1 find the equation of the tangent plane to the hyperboloid x 76355
Uploaded: 2022-03-28T20:21:22-08:00
Duration: 1 min 53 s
Channel: Ishana K
Description: the equation of the tangent plane to the ellipsoid x2a2 y2b2 z2c2 1 at the point x0 y0 z0 can be written as xx0 a2 yy0 b2 zz0 c2 1 find the equation of the tangent plane to the hyperboloid x 76355

          The equation of the tangent plane to the ellipsoid 
x^2/a^2 + y^2/b^2 + z^2/c^2 = 1
at the point 
(x0, y0, z0)
can be written as
xx0/a^2 + yy0/b^2 + zz0/c^2 = 1
Find the equation of the tangent plane to the
hyperboloid 
x^2/a^2 + y^2/b^2 - z^2/c^2 = 1
at 
(x0, y0, z0)
and express it in a form similar to the one for the
ellipsoid.

Added by Jose Francisco B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ishana K

03/28/2022

Step 1

∂(x^2/a^2 + y^2/b^2 - z^2/c^2)/∂x = 2x/a^2 ∂(x^2/a^2 + y^2/b^2 - z^2/c^2)/∂y = 2y/b^2 ∂(x^2/a^2 + y^2/b^2 - z^2/c^2)/∂z = -2z/c^2 Show more…

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The equation of the tangent plane to the ellipsoid x^2/a^2 + y^2/b^2 + z^2/c^2 = 1 at the point (x0, y0, z0) can be written as xx0/a^2 + yy0/b^2 + zz0/c^2 = 1 Find the equation of the tangent plane to the hyperboloid x^2/a^2 + y^2/b^2 - z^2/c^2 = 1 at (x0, y0, z0) and express it in a form similar to the one for the ellipsoid.