Q-23 (aT trajectories of the families of y? = 2ax, where a Find the orthogonal being a parameter.

Q: 1. Find the orthogonal trajectories of the family of curves x? + y2 = cy.

A:

Q: 3x* – 4y* = C

A: The given equation is: 3x4-4y4=c

Q: 3. Determine the coefficients a, b, c, d that will make the curve y = ax³ + bx? + cx +d have…

A: We will find the value of a, b, c, and d as following .

Q: 2x Find the orthogonal trajectories of the family of curves y = Ce" .

A:

Q: Find the orthogonal trajectories of y = ae" where a be the arbitrary constant.

A: The objective is to find the orthogonal trajectory of y=aex, where a be the arbitrary constant.…

Q: Find the orthogonal trajectories of the famil y of curves x'yxy=c where cis constant

A: Given:    x3y-xy3=c      Differentiating by using power rule we get…

Q: 5(a) Determine the orthogonal trajectories of the family of electric field lines described by the…

A: To find - Determine the orthogonal trajectories of the family of electric field lines described by…

Q: 1) 3 Find the orthogonal trajectories of the family of curves y = 2x+k

A: Please see the explanation below

Q: (6) Find the orthogonal trajectories of the family of curves r 4C cos 0, where C being %3D…

A: We have to solve given problem:

Q: y = x – 2 + Ce* X-

A:

Q: (6) Find the orthogonal trajectories of the 3C cos 0, where C family of curves r being parameter.

A: Answer

Q: Find the orthogonal trajectories of the curve x^(2) + y^(2) = c^(2)

A:

Q: (6) Find the orthogonal trajectories of the family of curves r= 2C cos 0, where C being parameter.

A: Consider the given curve. r=2Ccosθ          (1) Find the derivative of the given equation.…

Q: Find the orthogonal trajectories of the family of curves xy = a where a ≠ 0is an arbitrary constant.

A: Consider the equation: xy=Cy=Cxy'=-Cx2 Substitute the value of C in the first derivative:…

Q: Q 6. Find the orthogonal trajectories of the function y = x + ce-ª, which is passing through (-2, 0)

A:

Q: (6) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A: Orthogonal trajectory curve of a family of curve is defined as a curve which intersects every member…

Q: Find the orthogonal trajectories of the family y = 1 - sec?r + C 4

A:

Q: 3. Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle…

A: given family of parabolas y2=cx at angle θ=60° claim- find the family of oblique trajectories that…

Q: PART B: Find the Orthogonal Trajectories of the given family of curves. 8. y = c²(x² + 4y²);

A: Given curve is: y4=c2x2+4y2 To find the orthogonal trajectories of the given family of curves. From…

Q: SOWE FOR THE ORTHO GON AL TRAJECTORIES y² = 4x² (1-ex)

A:

Q: Find the orthogonal trajectories of x? + y? - 3Cx = 0.

A: If dydxis the slope of the tangent line then the slope of the orthogonal trajectory is -dxdy. So we…

Q: Find the orthogonal trajectories of a - =1; where 2 is an arbitrary parameter. a + 2

A: This is a question of the Differential equation.

Q: 4. Find the orthogonal trajectories of the family of curves y = Ce* +10

A: Given that : y = Ce2x + 10

Q: 4. Find the orthogonal trajectories of the family of parabola described by the equation (y– 3) = Cx.…

A: The solution of the problem is given in the next step.

Q: Q.2) Find the orthogonal trajectories of the family of curves e*(x sin y– y cos y) = c

A: 2 Given family of curves is e−xxsiny−ycosy=c. We have to find the orthogonal trajectories of the…

Q: PART C: Find the Orthogonal Trajectories of the given family of curves. 8. y = 4x°(1– cx);

A: We have to solve

Q: -y 5. e+eY = C %3D

A:

Q: Find the orthogonal trajectories to the family of curves: r=c- (in y -1).

A: Orthogonal trajectories can be find in the following way: (i) differentiate given family of curves,…

Q: Q.NO.2: a) Find the equation of the orthogonal trajectories of the family of curves. x²y² = 4c²

A:

Q: Find the equation of orthogonal trajectories of the given function 8x² + y² = c.

A:

Q: Q.2, a, Solve he initial valve problem * (2+x) dy + 2(1+x)y = 1+3x² y(-1) = 1 %3D by Find an…

A:

Q: 8. Find the orthogonal trajectories of y = cx CX

A:

Q: 2. Find the orthogonal trajectories of the family of curves x2 + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: Find the orthogonal trajectories of the family of curves y = ce^x. Select the correct response: x^2…

A:

Q: 02) Find the orthogonal trajectories for the family of curves given by x²y = k where parameter k is…

A: to find orthogonal trajectory we need to differentiate the equation and then replace dydxby…

Q: PART C: Find the Orthogonal Trajectories of the given family of curves. 8. y = 4x*(1 – cx);

A: The given equation is y2=4x21-cx. Find the orthogonal trajectories of the given family of the curve.

Q: 17. Determine the equation of the family of orthogonal trajectories of the the family of curves…

A: Given; y2=2x+c Now differentiate the given function with respect to x.…

Q: Find the orthogonal trajectories of y = e where a be the arbitrary constant.

A:

Q: Use the method of variation of parameters to produce a general solution of the inhomogenous equation…

A:

Q: 4) Find the orthogonal trajectories of the family of parabolas y – 3 = c(x + 1)².

A:

Q: Q-1 Find the orthogonal trajectories of y = ea" where a be the arbitrary constant. [

A: Given curve is y=eax

Q: Obtain the orthogonal trajectories of y=Cx^2 and compute for the positive value of y of the…

A:

Q: ind the orthogonal trajectories of the family of curve x2/3 +y2/3 =a2/3 where "a" is the parameter

A:

Q: 1. Find the orthogonal trajectories of the family of curve z + 3y = cy,where cis an arbitrary…

A: We will first find the differential equation of the of the given family of curves

Q: (6) Find the orthogonal trajectories of the family of curves r= 2C sin 0, where C being parameter.

A: See the detailed solution below.

Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2 = c^2. *

A: Curves:  x²+y²=c²

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.