Find the orthogonal trajectory of the given family of curves: 1. y = C (sec x + tan x) 2. x = C,es* %3D

Q: ) Find the orthogonal trajectory of the family of curve given by y = In(r³ + b)

A: First formulate a differential equation to eliminate the parameter b . Then replace (dy/dx) by…

Q: Find the orthogonal trajectory of the given family of curves. y=(ce^(x))/x

A: According to the given information it is required to find the orthogonal trajectory of the given…

Q: Find the orthogonal trajectory of y = c1(sec x + tan x)

A: Orthogonal trajectory: - Orthogonal trajectories can be defined as lines or curves that meet the…

Q: What is the angle between the curves y = x2 and y = x4 at their point of intersection?

A: We have find the angle between the curves y = x2 and y = x4 at their point of intersection we have,…

Q: Find equations of both the tangent lines to the ellipse x2 + 4y 36 that pass through the point (12,…

A: see below the calculation and answer

Q: = V4 cos" : – 1, y = 10 < x < 30

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Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t att-0. x =…

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Q: Find the orthogonal trajectory of the given family of curves. (x^2)+4xy+(y^2)=c

A: Given family of curve                                               x2+4xy+y2=c we have to find…

Q: Find orthogonal trajectory to the curve given by r = a(1 + cos θ)

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Q: Find the length of the curve described by y = V sec* t – 1 dt, - sI 4 4 (a) 4 (b) (c) (d) 2/2 (e) 1

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Q: Find the points on the parametric curve c(t) (3t2 - 5t, t3 - 10t) where the tangent line has slope…

A: Given curve is Firstly, we find dy/dx

Q: Find the equation for the tangent plane to the surface at the indicated point. -4x – y+ 2z = 1, P(1,…

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Q: Find the orthogonal trajectory of the given family of curves: 1. у%3DG;(sec x + tan x)

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Q: Show that the exact length of the curve below is y = Vr - r² – sin ¬1 (V7)

A: SOLUTION-

Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t at t = 0.…

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Q: Which of the following is the orthogonal trajectory of the family of 8. curves cz? + y? = 1?

A: Given: The given curve is cx2+y2=1

Q: A circle has a center at the origin and has a radius of R. If x = 10 and y = 20, determine the slope…

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Q: Given the curve y² = 5x – 1 at point ( 1,-2 ) , find the equation of tangent and normal to the…

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Q: Set up an intergral for the length of the curve, 04X y%3DZE* sin cx), O4 XE

A: Explanation of the answer is as follows

Q: Find a rectangular-coordinate equation for the curve x = 2cos(t) and y = 3sin(t), 0 <t < 2n.

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Q: If a curve C is given by r(t) = ⟨t, t2⟩ , what is | r'(t) | ?

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Q: Find the orthogonal trajectory of the family of curves x² + y² Cx

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Q: Find an equation of the curve that satisfies dy 20ya de and whose y-intercept is 3.

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Q: Find the orthogonal trajectory of the given family of curves. y=c*e^(2x)

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Q: The family of curves orthogonal to x2 + 4y2 = c2 has the general equation 04. %3D

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Q: Find the orthogonal trajectory of the given family of curves: 1. e* + e¬y = C1

A: We will solve the problem

Q: Find the orthogonal trajectory to the family of curves: y(x²+1) = Cx

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Q: Calculate a 3 ydz t 13x'y dy, Where Cis the oriented curve given in the figure . 3 Bydr+43xy dy =?…

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Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: Find the exact length of the curve. y = In(sec(x)), OsxSa/4

A: Length of a curve f(x) in interval [a,b] is given by ∫ab1+(f'(x))2dx

Q: Consider the curve y = zy+1. What is the value of- dz at (0, 1)? None of the given choices

A: The solution for the above question is as shown below.

Q: I. Find the acute angle between the given curves. 2. x'y+4a° y=8anx²=4 ay 3. x*y+4y=8Ax²y=4

A: We have to find the acute angle between the given curves: x2y+4y=8 and x2y=4

Q: Evaluate ∫с (x+y^1/2) ds, curve is given by figure 2

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Q: Find the tangent line(s) to the parametric curve given by a = t¹ - 9t² and y=t² at (0, 9).

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Q: Graph the curve. x 3e cos(t), y = 3e sin(t), 0stsn y y 30 X -60 -40 -20 20 -10 10 WebAssign Plot 20…

A: Given: x=3e^t cos(t) y=3e^t sin(t)

Q: Find the orthogonal trajectory. xy = k

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Q: Find the orthogonal trajectory to the family of curve given below y²=x²(1-Cx)

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Q: In which direction is the curve x = -2 sin t, y = 2 cos t, for 0 ≤ t &lt; 2π, generated?

A: x = -2 sin t, y = 2 cos t Table for values of x and y: t x y 0 0 2 π 0 -2 π2 2 0 2π 0 2

Q: Sketch the curves below by eliminating the parameter t. x = V3t + 4, y = 3t + 2

A: Given query is to sketch the curve by removing t.

Q: When finding the orthogonal trajectory of the family of curves y = k x³, we dy get dx 2x y Зу 2у 3x…

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Q: Find the orthogonal trajectory of the given family of curves: 1. y = C(sec x + tan x)

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Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = et, y = e-t

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Q: A circle has a center at the origin and has a radius of R. If x = 10 and y = 20, determine the slope…

A: Given that, There is a circle which center is at origin anf the radius is R. x = 10, y = 20 We have…

Q: Find the length of the arc of the curve in the given range, y3 1 x = 16y + 4y² + 3 0 <y< 4 - 4(y…

A: we have to find th length of the arc for the given curve .

Q: Find the length of parametrized curve given by  x(t) = 6t2 + 12t, y(t) = -4t3- 12t2 - 9t where t…

A: Consider the parametric curve given by: x(t)=6t2+12t and y(t)=-4t3-12t2-9t for t from 0 to 1. The…

Q: ind the orthogonal trajectory of the curve y? = ax²(1- cx); with a held fixed.

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Q: What is the equation of the plane that is tangent to the graph of z = x coS y – ye“, when (x, y) =…

A: Equation of the plane tangent to the surface z=f(x,y) :               Let   F(x,y,z) =0 ,then…

Q: 2) Find the cartesian eauation for the olar curve r=tan e sece ×ニy )yニxと 2.

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