14. Find a point on the surface z = 3x- y at which the tangent plane is parallel to the plane 6x + 4y- z = 5.

Q: Find the equation of the tangent plane (in the form z = ax + by +c where a, b, c are constants) to…

A: Here we use the formula of  ∂f∂x(a,b)(x-a)+∂f∂y(a,b)(y-b)=0 tangent plane to the surface at a point…

Q: ind the equation for the tangent plane to the surface z = In(6x2 +9y2 + 1) at the point (0,0, 0).…

A:

Q: 4. Find an equation of the tangent plane to the surface xyz = sin(x + y + z) at (1, −1,0).

A:

Q: The horizontal tangent plane of the surface z = 2x² – xy – y² + 6x – 6y – 2 is given by the equation…

A: Consider the given equation. z=2x2-xy-y2+6x-6y-2 Find the derivative with respect to x and y.…

Q: Find the equation of the tangent plane to the surface 4xe^yz+xz^2−7x^3y= 5 at(1,0,1).

A:

Q: Find the point(s) on the surface z = 3 − x2 − y2 + 6y, at which the tangent plane is horizontal.

A:

Q: (4) The equation of the tangent plane to the surface In = z²(x – 2y) + 3z +3 at (4, 2, –1) is 2y

A:

Q: Find the slope of the tangent line to the curve that is the intersection of the surface z = x2 - y2…

A: Calculate point of intersection and differentiate it to get the answer

Q: Find an equation of the tangent plane to the surface z = x2 + y2 + 3 at the given point( 2, 1, 8).

A: Known fact: Let F(x,y,z) be the surface which is differentiable at P(x0, y0, z0). then the equation…

Q: Find the equation for the tangent plane to the surface x- 5xyz+ y = - 7z at the point (- 1, -1, -…

A:

Q: Find the equation for the tangent plane to the surface x-9xyz +y= - 11z at the point (-1,-1,-1). O…

A: The given surface is x2-9xyz+y2=-11z2 and the point is -1,-1,-1.

Q: Find the slope of the tangent in the positive y-direction to the surface  z = 3x + 2y − 4exy at (4,…

A:

Q: Find the points at which the following surface has horizontal tangent planes: x² + 2y² + z2 – 2x –…

A:

Q: 9) Find a point on the surface z = 8- 3x2 - 2y2 at which the tangent plane is perpendicular to the…

A: In this question we have to find a point on the surface at which the tangent is perpendicular to the…

Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

Q: Find the slope of the tangent line to the curve of intersection of the surface z = x + y' with the…

A:

Q: Find an equation of the tangent plane to the surface z = 2x² + 1y² + læ + ly – 2 at the point (2, 5,…

A: This question is based on 3d geometry.

Q: Show that the line normal to the surface xy + z = 2 at the point (1, 1, 1) passes through the…

A:

Q: Find the points on the surface ry + yz + zx – x - 22 = 0 where the tangent plane is parallel to…

A: Given surface is  Fx, y, z=xy+yz+zx-x-z2 and we have to find the points on this surface where the…

Q: 4. Find both points on the surface xz – x2 – y? = 8 where the tangent plane is horizontal.

A:

Q: The equation of the tangent plane at the point P(1, 1,-1) on the surface z = f(x, y) = 4 - -* is x +…

A: As per bartleby guidelines we are supposed to answer only one question per post. This post contains…

Q: Find equations for the a) tangent line and b) normal plane to the curve made by the intersection of…

A: Given The given surfaces are 3x2y+y2z=-2 and 2xz-x2y=3.  The given point is 1,-1,1.

Q: What is the equation for the tangent plane to the surface z = 4x°y2 + 2y - 2 at the point P(1, -2,…

A:

Q: Find an equation of the tangent plane to the surface zx + 2xy + 3yz3 = 6 at a point in the…

A:

Q: 9) Find a point on the surface z= 8 – 3x² – 2y² at which the tangent plane is perpendicular to the…

A:

Q: Find the equation of the tangent plane to the surface z = In (2x + y) at the point (-1, 3, 0) . O x…

A: The equation of the tangent plane to the surface Z=fx,y atthe point a,b,fa,b is given by…

Q: Find the equation of tangent plane to the surface x^2 + 2y^2 + 3z^2 = 21 which is parallel to the…

A:

Q: Find a point on the surface z = 3x^2 − y^2 at which the tangent plane to this surface is parallel to…

A: We need to find the Point on the surface of  z=3x2−y2 given tangent plane to this surface is…

Q: 9. Show that the sum of the T-, y-, and z- intercepts of any tangent plane to the surface VI + Vỹ +…

A: Given, Gradient of the surface at any point (x0,y0,z0) is given by,

Q: The equation of the tangent plane to the surface defined by z y exp(-x) at the point (0, 1, 1) is =…

A: equation of the tangent plane

Q: Find the points on the surface xy + yz + zx – x – 22 = 0 where the tangent plane is parallel to…

A:

Q: Find the equation of the tangent plane to the surface f(x,y)=In(4x²-2xy-y²) at the point P(-1,-1,0).

A:

Q: Find an equation of the plane tangent to the surface xy z2 = 2 at the point (2, 1, -1). %3D

A: Given that XY3 Z2 =2 And point (2, 1,-1).

Q: Find the slope of the tangent in the positive y-direction to the surface z = 3x + 2y − 5exy at (3,…

A:

Q: 4. Determine all points on the surface x² + 2y² + 3z² + 2xy + 2yz = 1 in which the tangent plane of…

A:

Q: 9) Find a point on the surface z = 8 – 3x2 – 2y² at which the tangent plane is perpendicular to the…

A: Given, Surface, z=8-3x2-2y2 at which the tangent plane is perpendicular to the line…

Q: 3/Find the equation for the tangent plane and normal line to the surface Z=9-x² + y² at the point…

A:

Q: Find an equation of the tangent plane to the surface z = 24 3z+4y at the point (4,3, 1).

A: Use equation of tangent plane

Q: (b) Find the point that makes the tangent plane to the surface z = x- xy +y-2x + 4y horizontal.

A:

Q: Find the equation of the tangent plane to the given surface at the point (0,-1,2). y = 2x2 – z2 O y…

A:

Q: 3. Find an equation of the tangent plane to the surface z = 2xy + 4y xy-2x at the point (1,1,-6)

A:

Q: Find the equation of tangent plane to the surface z = ln (3x²) + 2y at A (1,0, In (3)).

A:

Q: Find the equation of the tangent plane to the surface determined by x'y* + z – 25 = 0 at x = 4, y =…

A:

Q: Find the equation of the tangent plane to the surface y = 2x - z at the point (0, -1,-2) y+2z = -5…

A:

Q: Find the angle of inclination of the tangent plane to the surface 3x2 + 2y2 − z = 15, at the given…

A: We have given surface 3x2+2y2-z=15 at point (2, 2, 5)   We have to find the angle of inclination…

Q: Find the equation of the tangent plane to the surface xy + 2yz + 3zx = 11 %3D at the point P (1, 1,…

A:

Q: Find the equation of the tangent plane to the surface y = 2x2 (0, –1, 2) z at the point O y+ 4z = 7…

A:

Q: 13. Find all points on the surface at which the tangent plane is horizontal. 3,,2 (a) z = x°y ² (b)…

A: