Obtain the dirfferential equation of the family of curves:  1. All circles passing through the origin and (0,4)

Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

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Q: Graph the curve r = 1 - cos θ in the Cartesian xy-plane

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Q: Consider the curve C parametrized by (x, y) = (3 cos (-10t), 3 sin(-10t)), for –x/2sts a/2 Then C is…

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Q: (b) Find a , b and c if the curvey = x + a x + b and y =c x + x have tangent lines paralle to each…

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Q: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: (a) Compute the arc (1,3, 1/3). F(t) = (t, 3, t) between the points (0,3, 0) and length of the curve

A: These 2 are unrelated problems as anyone can be solve without any help of another. So by Bartleby…

Q: Use the IVT to prove that the curves y = x2 and y = cos x intersect.

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Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: Compute F• dr for the oriented curve specified. F(x, y) = (9, y), quarter circle x² + y2 = 1 with x…

A: Given:

Q: Draw the following curves by extracting their points and then identifying their symmetries Y= Sin ()…

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Q: Compute F. dr for the oriented curve specified. F(x, y) = (4x², xy), line segment from (0, 0) to (2,…

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

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Q: sketch the given curves together in the appropriatecoordinate plane, and label each curve with its…

A: Draw graphs of y=ex and y=1ex

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

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Q: Compute Sc(2x + V) ds, where C is the curve from (0,0) to (2, 4) along y

A: Given

Q: Find the length of the curve x = 5-t, for 1 < t < 2. length = y = 3-t, z = 3t 5,

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

A: SOLUTION-

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 parametrization for the curve described below. the line segment with endpoints (5 - 1) and…

A: Given point :( 5 , -1 ) (10 , -6 )

Q: Consider the inmplicitly defined curve xy +3x2 4. %3D O Verify that the point (1, 1) is on the…

A: Consider, the implicitely defined curve                          xy2+3x2=4 We have to verify the…

Q: Express the following curves parametrically, including the interval for the parameter. 2.) 2.) A…

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Q: Graph the lemniscate curve r2 = sin 2θ in the Cartesian xy-plane

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Q: Straight lines with slope twice the x-intercept.

A: Let us assume x-intercept is a. That is, x = a when y  =0. So,  slope  =2a. Let us assume that the…

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: Find the path of the sloping path y = x² + c such that θ = π / 4 is the angle between the tangents…

A: Slope = 1  Point are (a,b) So equation of tangent      Y-b = 1.(x-a)

Q: Compute ∫C(2x+√y)ds, where Cis the curve from (0,0) to (2,4) along y=x^2.

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Q: Let C be the curve y = x³ – 3x2 + 4x – 1 joining the points (1, 1) and (2, 3). Find the value of…

A: We need to find value of integral.

Q: Find the length of the curve y=z from z 0 to z=4.

A: The length of the curve is given by:

Q: Trace the curve r = sinocos'o. 2)

A: Given: r=12sin3θcos3θ Explanation: r=12sinθcos3θat θ=0r=12sin0cos30=0⇒r=0at…

Q: Find the tangent plane to the equation z 2y cos(3r - 6y) at the point (6,3,6) %3D

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Q: Find the exact length of the curve. y = In(sec(x)), 0<x< 1/3 In (2 + v 2 ) – - In (1)

A: Since you have posted 2 questions we will solve one for you please resubmit the question. Given:…

Q: Explain why a cubic Bézier curve is completely determined by x(0), x (0), х(1), and x'(1).

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Q: Find an equation of the tangent plane to the surface at the given point. fx, у) %3 х2 - 2ху + у2,…

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Q: Give the equation of the tangent plane to each of these surfaces at the point indicated.

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Q: Find the exact length of the curve. y = In(sec(x)), Osxs- 6

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Q: Find a parametrization for the curve described below. the line segment with endpoints (4,1) and…

A: The line segments between  (xo , yo)  and  ( x1, y1)  can be expressed as:x(t) = (1 − t)xo + tx1…

Q: What is the integrating foc tor of the equation %3B

A: Topic:- differential equations

Q: Let R be the annulus defined by {1<x² +y² < 4}. Is R connected? Is it simply connected? Describe C =…

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Q: If x = 8cos3theta and y = 8sin3theta, find the total length of the curve swept out by the point…

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Q: Determine the orthogonal trajectories of the family of circles (equation below) that is tangent to…

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Q: Find the exact length of the curve. y = (1 + x*,3/2, OSxS 5

A: The curve is y=231+x232 , 0≤x≤5

Q: Obtain the dirfferential equation of the family of plain curves given 1. All circles passing…

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Q: Find the family of curves in the plane such that in each point P(x,y) of it, the intercept of its…

A: Write the equation of the tangent for the family of curves for any point P (x , y). Assume the slope…

Q: Find the diffrential equation of for each of the curves determined by the condition that at each…

A: length of subtangent =ydydx

Q: Consider the given curve: R(f) = (2 cos f, 12f +3,-2 sin f) Reparametrize the curve using arclength…

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Q: Find an equation for the tangent plane to z = 9x? – 8y² at the point (1, 1, 1). - = 0.

A: Here we find the equation of tangent plane.