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

Q: What are the coordinates of the points in the graph of y² –x²+ 6x – 13=0 in which the tangent line…

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Q: Find the equation of the tangent line to the curve at the given point. y = 5x – 2x, (1, 3) y =

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

A: We will find out the required solution.

Q: Find an equation of the tangent line to the curve y = x - 3x + 5x that has the least slope.

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Q: Find the equation of the tangent line to the curve y= (1+2x)2 at the point (2, 25). y = %3D

A: This question is based on application of Derivative.

Q: Show that the point (2, 4) lies on the curve x3 + y3 - 9xy = 0. Then find the tangent line and…

A: Given: f(x, y) = x3 + y3 - 9xy = 0 To find:  Equation of tangent and normal to the curve at point…

Q: Find an equation of the normal line to the curve  y = x  that is parallel to the line  4x + y = 1.

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Q: Find the orthogonal trajectories of the family of curves. Sketch several members of each family y =…

A: We have given the curve; y = mx

Q: 5. Find the equation of the tangent and normal line of 2x+1 y = at point (1,1). x+2

A: A detailed solution is given below     (As per our guidelines, we have to solve only one question)

Q: Find the derivative dydx of the Archimedean spiral.

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Q: Find the orthogonal trajectories of the family of curves.

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Q: Find the equation of the normal to the curve y=x²-x -2 at the point (1, -2)

A: Given curve , y=x2-x-2 we have to find the equation of the normal to the given curve at the point…

Q: Find equations of the tangent line and normal line to the curve y = x/x at the point (1, 1).…

A: y=xx

Q: What does it mean for two families of curves to be mutually orthogonal?

A: Two families of curve are said to be mutually orthogonal if they intersect at right angles. Angles…

Q: Find the orthogonal trajectories of the family of curves. Sketch several members of each Family y =…

A: The given equation of curve is. We have to find the orthogonal trajectories of family of curve.…

Q: Find the equation of the tangent line to the curve at the given point. y = /2x + 1, (4, 3) y =

A: See the attachment

Q: Find an eqaution of the tangent line to the curve at the given point. y = 4x - 3x2, (2,-4)

A: The given function is y=4x-3x2 and the point is 2,-4

Q: 6. Find the tangent line and normal line to curve y = x3 - 3x2 - 2 at point (1, -4)?

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Q: What point on the curve y = Vx is closest to the point (5, 0)?

A: Use distance formula between two point and then differentiate

Q: write an equation of the normal line to the curve y=x^3-3x+1 at the point (2,3)

A: To calculate the equation of the normal line to the curve, first we need to calculate the gradient…

Q: Find the curve in the xy-plane that passes through the point (9,4) and whose slope at each point is…

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Q: Find the equation of the tangent line to the curve at the given point.

A: To find the tangent at the given point on the curve, using derivatives

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 equation of the line normal to the curve x'y+ y'x = 10 at point (1,2).

A: Slope of a normal to the function y=f(x) at point m,n is given by the value of -dxdy at m,n Equation…

Q: Find the equation of the tangent line to the ellipse 25x2+ y2 = 109 at the point (2, 3

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Q: Find the equation for the perpendicular trajectories of the family. 1. x - curve

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Q: What is the length of the curve y3/2+4 from the point (1,5) to (4,12)?

A: To find: The length of the curve y3/2+4 from the point (1,5) to (4,12).

Q: Find equations of the tangent line and normal line tothe curve at the given point. y= 6Cosx  (π/3,…

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Q: Find the equations of the tangent line and normal line to the parabola y=2x2 at the point (2,8).

A: We find dy/dx at x=2 to find the slope of the tangent  Then we use the point-slope formula to find…

Q: Determine the equation of the normal line to the curve y= 2 − (1/3) x2 that is parallel to the line…

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Q: Find the equations of the tangent and the normal lines to the curve x5 + y5 = 4 x2y2 at the point…

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Q: y = xv16 + x², (0,0)

A: Topic:- application of derivatives

Q: Find the orthogonal trajectories to the family of curves:

A: Consider the given equation. x2=C-12y2lny2-1 Find the derivative of the function with respect to x.…

Q: What are the coordinates of the points in the graph of y2 – x² + 6x – 13= 0 in which the tangent…

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Q: Find the equation of normal to the curve y = 2x – 4x² +x- 6 at point (2,–4)

A: Given y=2x3-4x2+x-6 and point is P(2,-4)We need to find the slope i.e. y'dydx=ddx(2x3-4x2+x-6)We…

Q: Show that the curve y = 6x + 6x - 3 has no tangent line with slope 2.

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Q: Find equations of the tangent and normal line to the curve y (2x+1) %3D at x=2. (3x2-2)

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Q: A curve contains (3, 7) has slope of tangent line is 4x – 5. What is the curve equation?

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Q: Find the perpendicular trajectories of the family of y = ax" curves. N= -1, n=1 and Draw each curve…

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Q: Find the normal to the curve y = 1 - x2 at the point (3, -8).

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Q: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

A: As we know that; The slope of the horizontal tangent line is zero or m=dydxPx0,y0=0 Given;…

Q: calculate the slope of the tangent line to the curve 3x3y2-2y3=-4 at the point (1,2)

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Q: Find an equation of the normal line to the curve of y = x that is parallel to the line 6x + y = 1. y…

A: Draw the graph of the given curve and the given parallel line.

Q: Show that the curve y =6x3 +5x -3 has no tangentline with slope 4.

A: Consider the following equation of curve: y=6x3+5x-3 Differentiate y with respect to x:…

Q: Show that the curve y = 6 x 3 + 5x -3            has no tangent line with slope 4.

A: y=6x3+5x-3 has no tangent line with slope 4

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 equation of the normal to the curve y=x2-x-2 at the point (1,-2)

A: To find the normal to the curve.

Q: 4. Find the member of the curve whose slope at any point is 4y point (3, 4) and passes through the

A: Note: As they are different questions, as per our company guidelines we are supposed to answer the…