Find equations of the following. 2(x - 4)2 + (y - 1)2 + (2 – 6)2 = 10, (5, 3, 8) (a) the tangent plane (b) the normal line (x(e), y(e), 2(e)) =

Q: Find parametric equations for the normal line to the surfacez=-7x2 -9y2   at the point  (2,1,-37)

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Q: Q1) Find equation of line normal to plane 3x + 2y - z = 5 and pass through Origin point. 30 mark

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Q: Find an equation of the tangent plane to the surface at the given point. x² + y² – 9z2 = 4, (-2, -3,…

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Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 5  where the tangent line is horizontal. (x,…

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Q: What is the equation of the tangent line and the normal line to y = x2 – 4x + 2 at (4,2)…

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Q: 2. y2-xev-1+ x = 7 at (2,1)

A: Solution:Giveny2-xey-1+x3=7   at (2,1)To find the equation of normalFormula:Equation of…

Q: Find an equation of the normal line to the curve  y = x  that is parallel to the line  4x + y = 1.

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Q: (i) Find equations of the tangent plane and the normal line to the given surface at the specified…

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Q: 5. Find the equation of the tangent and normal line of 2x+1 y = at point (1,1). x+2

A: A detailed solution is given below     (As per our guidelines, we have to solve only one question)

Q: a) Find an equation of the tangent plane to the surface at the given point. xyz = 15, (1, 3, 5) b)…

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Q: Find the equation of tangent plane and normal lines of the surface: t the point (1,3, 2).

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Q: Find the equations of the tangent plane and the normal line at point (1,1,-2) to surface z^2 =…

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Q: Find the tangent plane and normal line from x2 + y2 + z2 = 30 in (1, -2, 5)

A: Given: -

Q: Find parametric equations for the normal line to the surfacez=ln(3x2 +7y2 +1)  at the point…

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Q: (a) Find the directional derivative of φ = x2 + sin y −xz in the direction i+ 2j−2k at the point (1,…

A: a) Given that φ=x2+siny-xz Now first evaluate gradient of φ, so…

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 4z2 = 21,    (−3,…

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Q: Q3A) Find normal line and parallel plane to the function f(x, y, z) = x²y²z² - 4 At point (1,-1,2).

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Q: Find the equations of the tangent and the normal of y = 3x2-2x+1 at point (1,2).

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Q: Find an equation of normal line to the curve y = Vx that is parallel to the line 2x+y = 4.

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Q: Find an equation of the normal line to the curve y = Vx that is parallel to the line 6x + y = 1. y =

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Q: Find the equation for the tangent plane and the normal line at the point Po(3,3,1) on the surface x…

A: To find an equation for the tangent plane and the normal line at the point (3,3,1).

Q: 8. Find the equations of the tangent plane and the normal line to y +z – x=2 at (-1, 1, 0).

A: Consider the given equation: y2+z2-x=2fx,y,z=y2+z2-x-2 Calculate the partial derivative with respect…

Q: 2 2 the equation of the tangent plane to the surface x² + y² + y² +2²= -1 at the point (2, -3, 4)

A: I am attaching image so that you understand each and every step.

Q: Find an equation of the normal line to the curve of y = Vx that is parallel to the line 6x + y = 1.…

A: Given that: The curve y = x parallel to the line 6x + y = 1 To find: The equation of normal line to…

Q: Find the equation of the normal line to the paraboloid z = 2x² +y² at the point (1,2,6). Select one:…

A: Equation of paraboloid  To find: The equation of normal at a point P = (1,2,6).

Q: Find the equation of the normal to the curve x2 + y2 = 5 at the point (2,1). a. y=2x b. x=y c. x=2y…

A: Given that

Q: b) Find equation of line passing the point ( 4, -1) and normal to 3y+ x=1. ||

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Q: Find the equations of tangent plane and normal line to the graph of 9yz – Vx² – 8z = xy² – 26 at the…

A: Find the direction derivative for the function f (x,y,z).…

Q: Find the equations of the tangent and the normal lines to the curve x5 + y5 = 4 x2y2 at the point…

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Q: Find the equation for the tangent plane and the normal line at the point Po(3,2,3) on the surface 2x…

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Q: 6. Where does the normal line to the curve y = x - x² at the point (1, 0) intersect the curve a…

A: Topic = Functions

Q: 6. Find an equation of the tangent plane and a set of symmetric equations of the normal line to the…

A: Let's find.

Q: Find an equation of the normal line to the curve of y = √x that is parallel to the line 2x + y = 1.…

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Q: Find an equation of the normal line to y = x2 at the point (2, 4). (The normal line at a point is…

A: y=x2 Differentiating with respect to x, we get dydx=2x Now slope of the tangent line at 2, 4 is,…

Q: Find the equation of normal to the curve y = 2x – 4x² +x- 6 at point (2,–4)

A: Given y=2x3-4x2+x-6 and point is P(2,-4)We need to find the slope i.e. y'dydx=ddx(2x3-4x2+x-6)We…

Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 3, 4) (b)…

A: Given: xyz=12 (1,3,4)

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 7z2 = 27,   (−3,…

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Q: Q1) Find equation of line normal to plane 3x + 2y - z = 5 and pass through Origin point.

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Q: 2. Find the equation of the tangent lines and the normal lines to the curve y = 2x² +3 at the point…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 14, (1,…

A: We have to solve given Questions.

Q: Find an equation of the tangent plane to the surface at the given point. x² + y2 + z2 = 33, (1, 4,…

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Q: Find the symmetric equations for the normal line Ly to the surface S: f(x,y)=5√√² + y² at the point…

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Q: 16. Find the equations of the tangent and normal lines to the curve 16x* + y* = 32 at its points of…

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Q: Find the orthogonal trajectory of the curve x^2 + y^2 = 2 ln x

A: See the details solution in below

Q: Find an equation of the tangent plane to the surface at the given point. x² + y2 – 5z2 = 140, (-8,…

A: We will solve the problem

Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x² - y², (5, 3, 16)…

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Q: Find all equations of normal line at the point (1, 1, –1) to the surface 2 +z² +3 = 2y + y?…

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Q: Find the equations of tangents & normal lines to the ff. curves using the stipulated conditions. 2.…

A: Solution Given 4x2+9y2=40, m=-29we need to find the equation of tangents & nomal lines