Find the equation of the tangent plane and normal line to the surface x^2/2-y^2/3=z at (2,3,-1)
Find the equation of the tangent plane and normal line to the surface x^2/2-y^2/3=z at (2,3,-1)
Juhi , 7 Years ago
Grade 12
Analytical Geometry> Find the equation of the tangent plane an...
1 Answers
Arun
Note that the tangent plane to the surface f(x,y,z) = k at (x0,y0,z0) is
z(x0,y0,z0)(x-x0) + fy(x0,y0,z0)(y-y0) + fz(x0,y0,z0)(z-z0) = 0.
fx(x,y,z) = ∂f(x,y,z)/∂x
= ∂(x2/2 - y2/3 - z)/∂x
= x
fy(x,y,z) = ∂f(x,y,z)/∂y
= - 2y/3
fz(x,y,z) = ∂f(x,y,z)/∂z
= -1
The gradient value at (2, 3, -1) is
∇f(2, 3, -1) = x(2, 3, -1), fy(2, 3, -1), fz(2, 3, -1)>
=
The tangent plane is given by
2(x - (2)) - 2(y - 3) -1 (z - (-1)) = 0
∴ 2x - 2y - z + 1= 0
Regards
Arun (askIITians forum expert)
Approved Last Activity: 7 Years ago
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Other Related Questions on analytical geometry
- The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
- The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
analytical geometry
1 Answer Available
Last Activity: 3 Years ago
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
analytical geometry
1 Answer Available
Last Activity: 3 Years ago
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
analytical geometry
1 Answer Available
Last Activity: 3 Years ago
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
analytical geometry
1 Answer Available
Last Activity: 3 Years ago