Find the equation of the tangent plane to the surface y = 2x2 - z at the point %3D (0, -1,-2) y+2z = -5 y – 2z = 3 %3D y+4z = -9 y – 4z = 7

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: Find the equation of the tangent plane to the given surface at the specified point. z=xsin(x+y),…

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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).

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Q: Find the equation for the tangent plane to the surface z=ln(4x2 +3y2 +1) at the point (0,0,0)

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Q: Find the equation of the plane tangent to the surface G(x,y, z) = 2x² - y² – 3z2 = -4 at P = (-2,…

A: Given surface is                                                G(x, y, z): 2x2-y2-3z2=-4 we have to…

Q: Find the slope of the tangent line at the point (1,−2,−3) on the curve of intersection of the…

A: Given surface is z=5-4x2-y2 The slope of tangent line to the curve that is the intersection of the…

Q: Find the general equation of the tangent plane to the surface x2 + y2 −2xy −x + 3yz = −4 at the…

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Q: What is the equation of the tangent plane to the surface y = eº cos (z) at the point (1, e, 0)?

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Q: Find an equation of the tangent plane to the surface S : za? – xy – yz = 18 at the point (0, –2, 3).…

A: We know that an equation of the tangent plane to the surface Fx, y, z at the point x0, y0, z0 is…

Q: Find the equation of the tangent plane to the surface defined by the function f(x, y) = x³…

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Q: 7. Find the equation of the tangent plane to the surface: x² + y* -z =i, at (2, 1,2)

A: Given : x2+y2-z2=12z

Q: 4. Find an equation of the tangent plane to the surface z = xy+8 at the point (1,1,-10) xy-2x

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = x sin(y – x),…

A: From the given equation: z=xsin(y-x) And Px,y,z=8,8,0 Let, f(x,y,z)=z-xsiny-x As we know that, The…

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. cos…

A: Given,

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, -…

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Q: Find an equation of the tangent plane to the surface z=−2x^2+3y^2−x+3y+1 at the point (1, 1, 4)…

A: We have to find the  equation of tangent plane

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

A: Given eq. of surface z=9-x2+y2 at the point 1,2,4             (1)

Q: Find an equation of the tangent plane to the surface at the given point. x^2 + 3y^2 + 4z^2 = 20, P =…

A: The equation of the tangent plane can be calculated by using the formula…

Q: Find an equation of the tangent plane to the surface 4x^2 + 9y^2 − z^2 = 14 at P = (2, 1, 4).

A: Given,4x2+9y2-z2=14at P=(2,1,4)

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

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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: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. x2…

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Q: Find the equation for the tangent plane to the surface z = Vy -x at the point (2,3,1). Use a…

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Q: Find an equation of the tangent plane to the given surface at the specified point. 3Vy Z = VY, (-1,…

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Q: 4. Find an equation of the tangent plane to the surface z=- xy+8 at the point (1,1,-10) ху — 2х

A: Equation of tangent plane is: {df(x0,y0)/dx} (x-x0)+{df(x0,y0)/dy} (y-y0)-(z-z0)=0

Q: Find an equation of the tangent plane to the given surface at the specified point. f(x,y) =…

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Q: Find the equation of the tangent plane to the surface 2 = r - 2r'y+ 2r y at the point where x = 1…

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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).

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Q: Find the equation of the tangent plane to the surface x^2e^z+xyz+y= 3 at the point (1,2,0)

A: Find the equation of the tangent plane to the surface x^2e^z+xyz+y= 3 at the point (1,2,0)

Q: 3. Find an equation of the tangent plane at P = (0, 3, –1) to the surface with equation ze" + elz+1)…

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = (xy)^1/2,…

A: We know that tangent plane to the surface z=f(x,y) at point (a,b,c) is

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

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

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

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Q: Find an equation of the tangent plane to the given surface at the specified point. 3.  z = 2x2 + y2…

A: Given that: z = 2x2 + y2 - 5y, (1, 2, -4)

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

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Q: 4. Find the equation of the tangent plane to the level surface x4 + yz – yz² + 5x = 0 at 3

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Q: Find an equation for the tangent plane to the surface given by f(x,y)=÷(4x² – 2y²) at the point…

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Q: Find the equation of the tangent plane to the surface z = 4.x*y? + 2y at point (1, -2, 12).

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

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Q: Find an equation of the plane tangent to the surface f(x, y) = xy² – 5x at the poin (1, 2, –1).

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: Find the equation of the tangent plane to the surface z = xy at the point (1, 2, 2) and to the…

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Q: Find an equation of the tangent plane to the surface z = xy at (1,2,2).

A: The given surface can be written as F(x, y, z)=0, where F(x, y, z)=xy-z

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

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Q: Find the equation of the tangent plane to the surface z =e/ In (2y) at the point (2, 4,1.643). Note:…

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

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Q: Find the equation of the tangent plane to the surface 4. =1 at the point 16 9. (1,-3,2) O a.…

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = V xy, (2, 2,…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.