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

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: Determine the angle between the curves 2x=y2 and x2+y2-5x=0

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

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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: Find the exact length of the curve. 글 cosh(2x), sxs8 y = 4 +

A: Given:

Q: Find the orthogonal trajectory. y = ke-Sx

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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: Verify that the following pairs of curves meet orthogonally x2 + y2 = 4, x2 = 3y2

A: The slope of the tangent of x2 + y2 = 4  is  The slope of the tangent of x2 = 3y2  is

Q: Find the ponits on the curve 9y2 =x3 where normal to the curve makes equal intercepts with axes

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Q: Find the slope of the line normal to the curve y = x³ - 2x +1 at x = 2 -

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Q: Find the equations of all tangent lines to the curve x² + 4y2 = 8 that pass through the %3D point…

A: The curve x2+4y2=8 that pass through the point (-4, 0). We have to find the equation of all tangent…

Q: Find the equation of the tangent line to the curve y = x+5x* which is passing through point (1, 3):*…

A: Given : Curve  y = x + 5x2 Point 1,3   To find : The equation of the tangent line to the given…

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: 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: dy 20 yx %3D

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Q: Find point on the ellipse x^2+2y^2=1  where the tangent line has a slope of 1.

A: We know, slope of tangent line = dydx

Q: What is an orthogonal trajectory of a family of curves? Describe how one is found for a given family…

A: There are some conditions for the orthogonal trajectories.

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

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Q: Find thepoints on the curve y = 2x3 - 3x2 - 12x + 20 where thetangent line is perpendicular to the…

A: Given: The curve is y = 2x3 - 3x2 - 12x + 20 and the tangent line is perpendicular to the line y =…

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: zejz dz, 22 – 5z +4

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Q: Determine the equation of the line tangent to the curve   at the point (-1,1) and reestablish a…

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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 the ponits on the curve 9y2=x3 where normal to the curve makes equal intercepts with axes

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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: Verify that the following pairs of curves meet orthogonally x = 1 - y2, x = 1/3y2

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

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Q: Make the curve y=ax³ +bx²+cx+d pass though (0,3) and have at (1,2) a point of inflection with a…

A: Given: T curve y=ax3+bx2+cx+d passes through the point (0, 3). The point of inflection is (1, 2)…

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: Evaluate (2 - xy) ds where C is the curve given below. -2 -1 -2

A: Given   ∫C2-xyds Curve C

Q: Use the guideline of this section to sketch the curve 1. y = 1 + 1/x + 1/(x ^ 2)

A: To Sketch: y=1+1x+1x2 Explanation: (a). Domain and Range y=1+1x+1x2is defined everywhere except…

Q: Find the orthogonal trajectory. xy = k

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Q: find the equation of the secant lines of y=√x passing through the points: x1=1 and x2=2

A: Secant line for a function between two points on a curve is simply a straight line passing through…

Q: is an arbitrary constant Orthogonal Trajectory:

A: First we derivative the given equation then form differential equation of orthogonal trajectory.

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

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

A: See the details solution in below

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

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

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Q: . Determine the points where the curve 6x+ 4y-y=6 has a vertical tangent line. p. Does the curve…

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Q: Find the equation of the line that is normal to the curve (y-x)2 = 2x + 4 at (6,2). %3D

A: Use equation of normal line

Q: Find the equation of the line normal to the curve 2x^2-3xy+y-18=0 at (3,0).

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