Find the orthogonal trajectories of the family of curves y3 = 3(x – c). Draw a few representative curves of each family.

Q: 4. Find the orthogonal trajectories of the given family of curves. y = cx'.

A: Solution:-              y=cx3 →          1              Diff. w.r.t x            ⇒dydx=3cx2…

Q: 1. Find the orthogonal trajectories of the family of curves x? + y2 = cy.

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Q: Find the orthogonal trajectories of the family of curves y=Ce* +10

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Q: 5. e+ e = C1 %3D

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Q: 2x Find the orthogonal trajectories of the family of curves y = Ce" .

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Q: Find the length of the curve /- y = Vcos 2t dt from x = 0 to x = "/4.

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Q: Find the value of the number such that the families of curves  y =(x+c) -1  and y = a ( x+k) 1/3 are…

A: Given,

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

A: Given that: y2=x3a-x

Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) 2y³ + 3x² = C (F) 2y³ + x³…

A: Introduction: An orthogonal trajectory of the family is any curve that cuts each member of a…

Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: 2ys = Cx

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Q: Find the orthogonal trajectories of the family of curves. Use a graphing device to draw several…

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Q: Find the orthogonal trajectories of the given family of curves x - 4y c.

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Q: (6) Find the orthogonal trajectories of the family of curves r= 2C cos 0, where C being parameter.

A: Consider the given curve. r=2Ccosθ          (1) Find the derivative of the given equation.…

Q: Find the orthogonal trajectories of the family of curves r² + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: Q2/ Find the orthogonal trajectories of the family of curves x-y - c² YAS

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Q: Find the orthogonal trajectories of the functiony x + ce which is passing through (-2,0)

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Q: 2. Find the family of orthogonal trajectories of the given family of curves in the following…

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Q: Find the orthogonal trajectories of the family of curves x when 'a' is the parameter. +y Da

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Q: find the orthogonal trajectories of the family ofcurves. Sketch several members of each family. y =…

A: Consider the provided curve, y=cx2 Find the orthogonal trajectories of the family ofcurves. First…

Q: 4. Find the orthogonal trajectories of the family of curves y=Ce*™ +10

A: We have to find the orthogonal trajectories of the family of curves

Q: PART B: Find the Orthogonal Trajectories of the given family of curves. 8. y = c²(x² + 4y²);

A: Given curve is: y4=c2x2+4y2 To find the orthogonal trajectories of the given family of curves. From…

Q: 7

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Q: Find the length of the curve y = 1 - e^-x, 0 <=x<=1.

A: The given curve is

Q: 4. Find the orthogonal trajectories of the family of parabola described by the equation (y– 3) = Cx.…

A: The solution of the problem is given in the next step.

Q: (6) Find the orthogonal trajectories for the given families of curves 2x2 – 7y = c.

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Q: Find the orthogonal trajectories of the given family of curves. Draw a few representative curves of…

A: For the solution of the problem follow the next steps.

Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: 1. Find the orthogonal trajectories of the given family of curves: Circles through the origin with…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: PART C: Find the Orthogonal Trajectories of the given family of curves. 8. y = 4x°(1– cx);

A: We have to solve

Q: y6 = C (x² + 1) %3D

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Q: Find the orthog onal trajectories of the circles x+y - ay = 0, where a is a parameter.

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Q: -y 5. e+eY = C %3D

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Q: 6. Given that k is an arbitrary constant, find the orthogonal trajectories of the following family…

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Q: (4) Find the orthogonal trajectories of the family of curves z +y 2C?, where C being %3D a…

A: Note:-    as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2% D c^2. *

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Q: (4) Find the orthogonal trajectories of the family of curves z +y = 20C?, where C being %3D a…

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Q: Find the orthogonal trajectories of the family of curves x² + Y? = R? %3D

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

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Q: 02) Find the orthogonal trajectories for the family of curves given by x²y = k where parameter k is…

A: to find orthogonal trajectory we need to differentiate the equation and then replace dydxby…

Q: Which of the following is the isogonal trajectories of the one-parameter family of curves y(x-a) = 1…

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Q: PART C: Find the Orthogonal Trajectories of the given family of curves. 8. y = 4x*(1 – cx);

A: The given equation is y2=4x21-cx. Find the orthogonal trajectories of the given family of the curve.

Q: (B) Find the length of the curve y 4 -Inx for 1<x <3

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Q: Find the length of the curve y Inx at (2<x< 4)?

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Q: ind the orthogonal trajectories of the family of curve x2/3 +y2/3 =a2/3 where "a" is the parameter

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Q: Find the isogonal trajectories to a family of straight lines y= cx that cut the lines of the given…

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

A: The orthogonal trajectory is the family of curves that is perpendicular to the given curve. The…

Q: Find the family of orthogonal trajectories of the given family of curves in the following equation…

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Q: find the under the curve y=7-t^2 and above the t-axis

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