4. obtain the differential equation of the family of plane curves describe and sketch several representative members of the family. Parabolas with vertex and focus on the x-axis.

Q: 14) The curve given in parametric form by et +1 e2t – 3 with tER is a solution of the differential…

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Q: , find the differential equation for the following families of curves. 9. All circles.

A: The standard equation of the circle is: (x-h)2+(y-k)2=r2        ....(1) The center of the circle is…

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Q: What is the differential equation of the family of circles with their centers on the х — ахis ?

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Q: What is the differential equation of the family of parabolas having their vertices at the origin and…

A: The general equation of the parabola that has the focus on the y-axis is defined using the formula…

Q: Find the differential equation of the families of circles with center at (2, k) and with radius r.

A: Given,           The differential equation of the families of circles with center ar 2,k and with…

Q: B. Solve for the differential equation of the following families of curves: (1) Family of parabolas…

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Q: find the differential equation of the family of curves: strophoids r= a(sec + tan theta) in…

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Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 0, y = a sin 20 from 8 =…

A: We are asked to find the length of the curve whose parametric equations are as follows:…

Q: #3. Find parametric equations for the tangent line to thể curve with parametric equations x = (sin…

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Q: Determine the differential equation of the family of circles with center on the y axis

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Q: Find the differential equation for the following families of curves. 1. All circles. 2. Horizontal…

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Q: Find the differential equation of the family of hyperbolas having center at C(0, k), whose…

A: First write the standard equation of hyperbole having transverse axis parallel to y-axis and satisfy…

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint); + In…

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Q: (a) Find the differential equation of the family of spheres of radius r with Centre on the xy-plane…

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Q: b. Using differential equations, find the orthogonal trajectories of the following family of curves:…

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Q: Find the differential equation of the the following family of curves 1. Circles with center at the…

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Q: Find the differential equation for the family of parabolas with axis parallel to the x-axis and with…

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Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint)j + In…

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Q: Obtain the differential equation of the family of circles with centers at the x-axis. O yy" – (y)³…

A: Here we have to find differntial equation Family of circle with Centre at X axis

Q: at

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Q: 2. Find the differential equation of the family of circles having their center on the y-axis.

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Q: FInd the differential equation of the family of circle with center at the origin

A: We need to differentiate the given curve equation as Number of arbitrary constant present in…

Q: Determine the general parametric solution of the following unsolved differential equations for the…

A: See the details solution in below

Q: Find the differential equation of the family of ellipses with center at the origin a and the major…

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Q: find the differential equation for the following families of curves. 11. Hyperbolas with vertical…

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Q: (a) Find the differential equation of the family of spheres of radius r with Centre on the xy-plane…

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Q: Find the differential equation of a family of circles, each having its center on the line y=z and…

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Q: The differential equation of the family of hyperbolas with horizontal transverse axis and with…

A: Please check step 2 for solution.

Q: What are the order and degree of the differential equation representing the family of parabolas y2 =…

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Q: Find the differential equation described by the following family of curves. Ellipses having center…

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Q: Find the differential equation of a family of circles, each having its center on the line y = x and…

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Q: Find the differential equation of the the following family of curves All straight lines at a unit…

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Q: Determine if the point x = 0 is an ordinary point, a regular singular point, or an irregular…

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Q: The differential equation of the family of hyperbolas with horizontal transverse axis and with…

A: Here is the solution of the given problem.

Q: Obtain the differential equation of the families of parabolas with vertex and focus on the y-axis. O…

A: Explanation of the answer is as follows

Q: 10. Find the equations of the two tangent lines at the (-1,0) for the parametric curve x = 12- 2, y…

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Q: Find the differential equation of a family of circles, each having its center on the line y x and…

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Q: The differential equation of the family of hyperbolas with horizontal transverse axis and with…

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Q: Find the differential equations for each family of curves under the following conditions: a)…

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Q: 1. Find the differential equation of the family of hyperbolas having center at C(0, k), whose…

A: It is given that the hyperbola having center at C(0,k) and it's transverse axis is parallel to y…

Q: In each exercise, obtain the differential equation of plane curves described and sketch several…

A: Since you have asked multiple question, we will solve the first question for you .If you want any…

Q: 31. Find parametric equations for the tangent line to the curve of intersection of the cylinders x2…

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Q: Obtain the differential equation of the family of plane curves described and sketch several…

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Q: 8. Solve for the critical points of the parametric equations x = t - 1,y = t² +t

A: To find the critical points of parametric curve x(t)=t2-1, y(t)=t2+t

Q: 7- A sinusoidal curve has a minim um point at (-t/3, 5) and the closest maximum point to the right…

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Q: Obtain the differential Equation from the family of ellipses centered at (h.k) whose semi-major axis…

A: Here h,k are parameters ,not constant.

Q: Find the corresponding differential equation for the following family of curves. 1. All Straight…

A: The general equation of the family of straight line is given by y=mx+b, where m and b are arbitrary…

Q: 1. Obtain the differential equation of the family of plane curves described and sketch several…

A: To find:- Differential equation of family of circle with center at point (1, -2)

Q: X cor²y dx = tany du 3. yln xInydx +dy

A: