Find the orthogonal trajectories of the given family of curves y? = tcx 1-cx

Q: Find the orthogonal trajectories of the family of curves y^3 = 3(? − ?). Draw a few representative…

A: We will find out the required solution.

Q: Find the orthogonal trajectories of the family of curves. Sketch several members of each Family y =…

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Q: Find the points where the tangent line to y =2+4 is horizontal (Critical points)

A: We need to find points where the tangent line to y=xx2+4 is horizontal. In other words, we need to…

Q: Find the orthogonal trajectories of the given family of curves: a. Circles through the origin with…

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Q: Find the orthogonal trajectories of the curve family ?

A: Given equation: y=x-2+Ce-x

Q: Find the orthogonal trajectories for the family of curves 6x² + y² -9ax=0.

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Q: 4. x( 4x + 3y) = a

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Q: Find the orthogonal trajectories of the family of curves y = ax² + 4ax + 4a, where a being…

A: Orthogonal trajectory: If a curve cuts every member of a given family of curves at right angle, then…

Q: Find the orthogonal trajectories of the family of curves. Sketch several members of each family y =…

A: We have given the curve; y = mx

Q: Find the length of curve - Vsec*t-1 dt -<ys=

A: To find- Find the length of curve x = ∫0ysec4t - 1 dt, -π4 ≤ y ≤ π4

Q: How many horizontal tangent lines does the curve parametrized by the equations z(t) =-4t-1,…

A: on doing derivative we get the 1

Q: Find the orthogonal trajectories of the family of curves.

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Q: Find the equation for the perpendicular trajectories of the curve family. 1. x -

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Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

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Q: Find the equation for the y perpendicular trajectories of the curve family. 1. x

A: perpendicular trajectory

Q: y = 3x – 1 + Ce-3x | x = Cey?

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Q: Find the orthogonal trajectories of the family of curves. Sketch several members of each Family y =…

A: The given equation of curve is. We have to find the orthogonal trajectories of family of curve.…

Q: Find the orthogonal trajectories for the family of curves y=c1x4

A: First of all rearrange the given equation in such a way that both the variables be on one side of…

Q: Make the curve y= ax2+bx+c pass through (2,1) and be tangent to the lane y= 2x +4 at (1,6)

A: The given curve passes through (2,1) ⇒1=4a+2b+c                                    (1) And the curve…

Q: The point on the curve y=vx+2 which is closest to the point (5,2) is

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Q: Find the equation of the tangent plane to z = In(x²y) – x/ỹ at (-,4).

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Q: Find the equation of the tangent plane to z at (-4,2).

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Q: Find the orthogonal trajectories of the given family of curves: Circles through the origin with…

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Q: Find the point (xo,yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent line…

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Q: Find the orthogonal trajectories for the family of curves y2 = Cx3 . Use a graphing utility to graph…

A: Given curve is y2=Cx3.

Q: 10. y = Ce 2x

A: We have to find  orthogonal trajectory

Q: Find the average velocity of the function over the given interval. y= - 3x? - x, [5,6] – X,

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Q: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: Find the point (xo, yo) on the graph of y = x + 3x² + 4x – 5, at which the slope of the tangent line…

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Q: Find the equation for the perpendicular trajectories of the family. 1. x - curve

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Q: ; Find the equation of the tangent and normal line of the function f(x): V2x – 1 at the point (5,…

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Q: Find the orthogonal trajectories ofthe family of curves: y = ke*

A: As per our company guidelines we are supposed to answer only first question. Kindly repost rest of…

Q: Find the orthogonal trajectories to the family of curves:

A: Consider the given equation. x2=C-12y2lny2-1 Find the derivative of the function with respect to x.…

Q: The tangent line to the curve ³ + y³ = 9xy at the point (4,2) intersects the y-axis at y = -1. -2.…

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Q: determine the equation of the orthogonal trajectories of the following families curves: Straight…

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Q: Find an equation of the tangent plane to the graph z = Væ + y³ nt (8, 2, 4).

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

Q: 6. y C Sin x

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Q: 9. y = x'(1- cx ) %3D

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Q: Find the perpendicular trajectories of the family of y = ax" curves. N= -1, n=1 and Draw each curve…

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Q: Find the equation of the tangent line on 3xe™v² - ez 2ye at (1,1)

A: Given  3xexy2-ex3=2yex2first we find dydx at point (1,1)

Q: .2 7. y= cx

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Q: Find an equation of the tangent plane at the given point. z = In(x-2y), (3,1,0)

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Q: Find the equation of the tangent plane to z=6x2+2y2  at the point (1,5)

A: Given  z = 6x2+2y2  at the point (1,5)

Q: Find the points on the curve y = 2x3 + 3x? – 12x + 9 where the tangent line is horizontal. (x, y) =…

A: we have to find the points on the curve where the tangent line is horizontal. y=2x3+3x2-12x+9

Q: Please answer number 9 .determine the equation of the orthogonal trajectories of the following…

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Q: Please answer number 5 determine the equation of the orthogonal trajectories of the following…

A: Given that        ex + e-y = C1 Here we have to find the equation of the orthogonal trajectories.

Q: Find the equation s for the perpendicular trajectories of the curve family. 1. x -

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Q: Find an equation of the tangent line at the given point. 2x1/2 + 4y −1/2 = xy, (1, 4)

A: Given,

Q: Find the orthogonal trajectories to the family of curves: -1).

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.