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

Q: Find the equation of the Bézier curve with control points P0 = (−1,−1), P1 = (−1, 1), P2 = (1, 1),…

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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: 5) Find the orthogonal trajectory of the family of curve given by y = In(r+b) %3D

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Q: I Find the acute angle between the two curves xy = 3 and x2 = 9y

A: Given data: First curve xy=3. Second curve x2=9y.

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: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: calculate |(3y-VE)ds where C is the curve

A: In this question, we evaluate the integral by parametrization of the curves the integral is…

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: The direction field of the DE y' + ye³x+7 = −2y² will have a line segment with positive slope at the…

A: Given y'+ye^(3x+7)=-2y² We know that the dy/dx gives the direction field. Hence the given DE can be…

Q: Suppose a curve is defined by the equation 16(x² + y²) = 45. Show that if you translate the curve to…

A: Use the shifting properties of a curve and form the new equation.

Q: Evaluate [(x +2y) ds, where C is the curve defined by y = √√4 – æ², for x = [0, 1

A: Here ds is arc length.

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

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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: What isfor the curve given by x = (t – 1)³ and y = vt ? | dx 1 2VE 6VE(t-1)2 3(t-1)2 O Option 4…

A: Using chain rule of differentiation

Q: Find the exact length of the curve. Vy (y - 3), 16 < y < 25 X =

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

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Q: If the line r = (2-t, -2 + 13t, 8t) is the normal tangent line to the level surface axyz²by² = -14…

A: answer is in next step . please give a like !!

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

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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: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: Given Data The equation is:  The point is: (-2,1)   Substitute the point (-2, 1) in the given…

Q: Find orthogoral trajectory to the family of dircles 3 x² + y? = 2Cy.

A: We have given equation of curve x2+y2=2Cy Then, differentiate both sides we get…

Q: dy Find for the curve x-2.x'y-20y 2 at point (-2,1). de

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Q: Find the orthogonal trajectory of the curve a2 + y² = 2ln cx

A: The given family of curve is                                           x2+y2=2 ln(cx)

Q: Find the orthogonal trajectory of the family of y=ax

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

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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: 4. Evaluate S. y² – 3z + 2 ds for each of the following curve C is the line segment from (1,0,4) to…

A: We have ∫Cy2-3z+2 ds C is the line segment from 1,0,4 to 2,-1,1 Now, the parametric equation of the…

Q: What are the coordinates of the points in the graph of y – z² + 6z – 13 = 0 in which the tangent…

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Q: D. Obtain the or thagonal trajectory of the family of ax+x =5+y3. aur ves of

A: Explanation of the answer is as follows

Q: 36y2 = (x2 − 4)3,    2 ≤ x ≤ 6,    y ≥ 0

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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: 1. Find the equations of tangent and normal lines to the curve whose equation y2 – 6x2 + 4y + 19 = 0…

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Q: Show that the curves 2x2 + 3y2 = 5 and y2 = x3 are orthogonal.

A: To show that the two curves are orthogonal.

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

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

A: Given query is to find the orthogonal trajectory of the curve.

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 orthogonal trajectory of the family of curve, x² = C1y³.

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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 the family of curves orthogonal to the family 4y2 + 3x2 = k when x > 0 and y > 0. (A) 3y2 – 4x2…

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Q: 3. Find the orthogonal trajectory of the given family of curve x2 + y² = C1

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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: Suppose the curve y =x4 +ax3+ bx2+ cx +d has atangent line when x=0  with equation y= 2x +1 and…

A: Given the curve is   y =x4 +ax3+ bx2+ cx +d Differentiating with respect to "x" y' = 4x3 + 3ax2 +…

Q: The orthogonal trajectory of the 1-parameter family of curves, y = cr will be given by: r² + y? = c…

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Q: Evaluate (2x+2y)ds if the curve C is given by F(t)=(2t²)ī +(1²)j, 0≤t≤1.

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Q: Which of the following straight lines are tangent to the curve y = x³ + 4x2 + 7x and passes through…

A: Topic = Geometry  y=7x ia the tangent to the curve.

Q: Find the paths orthogonal to the family of curves: cy ^ 2 = xe ^ x

A: Orthogonal path is a curve if it cuts every member of a given family of curves at right angles.