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

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: The length of the curve defined parametrically by: x = e*cost, y = e' sint, 0 Sts is equal to:…

A:

Q: Find the points on the parametric curve c(t) = (3t2 − 2t, t3 − 6t) where the tangent line has slope…

A: Given curve: So,

Q: Sketch the path using the following parametric equations x(t) = 3t – 7 and y(t) = 4 sin t+1 0st55,…

A: Here we need to find different points for different values of t

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

A:

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

A:

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

A:

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: 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 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: The parametric equation of a curve is given by x= cost, y= sint− cost, 0 ≤ t ≤ 1 . Without…

A:

Q: Calculate F.dr, where C is the curve given by ti + 123+ tk, with t = [0, 1] and F(x, y, z) = 4xei +…

A:

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

A:

Q: Find the slope of the curve whose parametric equation is given by y = t³ + t²+ 1/t and x = t⁴ + 3t²…

A:

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: Given the curve with parametric equations, find the slope and the equation of the tangent line at…

A: Here we have to find the Slope of tangent line at indicated points . We are given parametric…

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

A:

Q: Consider the parametric curve given by x = t2 + 5, y= e* est + 2t. 3t Find the slope of the tangent…

A:

Q: Prove that the curve y: (-,-)→ R³ is regular with factor H and determine whether the image y (t) =…

A: If γ't not equal to 0 for all t∈-π2,π2then it is regular. If γ''t=kγ't for all t∈-π2,π2 then the…

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

A:

Q: Find the tangent line(s) to the parametric curve given by a = t5 – 4t3 y = t? at (0, 4).

A: Find the tangent line(s) to the parametric curve given by x = t^5-4t^3 , y = t^2 at (0,4).

Q: Sketch the two curves 7(t) = tî + t²j; t e [1, 5] and B(T) = e"î + e²r3; T E [0, In 5]. How are they…

A:

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

A:

Q: 19. Evaluate Scx ds, where C is a. the straight-line segment x = t, y = t/2, from (0, 0) to (4, 2).…

A: Part (a)

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

A:

Q: a) Given a curve y = px* + 2x has turning point at (–1,q). Find the value of p and q.

A:

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

A: We will solve the problem

Q: What is the slope at t = −2 ?

A:

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: Given that the line y =r- b is an asymptote to the ar curve y a,b €R,r = 1, then b = I-1 -1-a B 1-a…

A:

Q: Find the points on the parametric curve c(t) = (3t 2 − 2t,t 3 − 6t)where the tangent line has slope…

A: This question is taken from the tangent and normal in which we have to find points on the given…

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

A:

Q: Find the exact length of the given parametric curve. X = = 8t³, y = 12t², 0 <t< 2

A: Consider the parametric equations

Q: find the orthogonal trajectory of the family of curves r^n = a sin n theta

A:

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

A: Given   ∫C2-xyds Curve C

Q: A curve C is defined by the parametric equations x(t) y(t) = 8t³ – 2t² + 4. Write the equation of…

A:

Q: Find the orthogonal trajectory. xy = k

A:

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

A:

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

A:

Q: Let Sketch the curve and find the length of this curve. r(t) = (t, 3 cost, 3 sin t), 0≤ t ≤ 2π.

A:

Q: The given curve is rotated y = 3 - x2,

A:

Q: x = +4r2 +4t +1 y =1+3 at the point P(1, 1).

A:

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

A:

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

A:

Q: Find the isogonal trajectory of the family of curves y + 2xy – x² = k where tan a = 1

A:

Q: Find the orthogonal trajectory of y=c cos x.

A: