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Solution: Tangent planes for F(x, y, z) = 0 Find an equation
Chapter 10, Problem 10E(choose chapter or problem)
Tangent planes for F(x,y,z) = 0 Find an equation of the plane tangent to the following surfaces at the given points.
\(x^{2}+y^{2}-z^{2}=0\); (3,4,5) and (-4,-3,5)
Questions & Answers
QUESTION:
Tangent planes for F(x,y,z) = 0 Find an equation of the plane tangent to the following surfaces at the given points.
\(x^{2}+y^{2}-z^{2}=0\); (3,4,5) and (-4,-3,5)
ANSWER:Solution :Step 1: we can visualize the line tangent to a curve at a point in 2-space, we can picture the plane tangent to a surface at a pointConsider the given surface by z=f(x,y), let (x0,y0,z0) be any point on this surface, if f(x,y) is differentiable at (x0,y0), then the surface has a tangent plane at (x0,y0,z0). The equation of the tangent plane is :fx(x0 y0)(xx0)+fy(x0 y0)(yy0)(zz0)=0