2. Find the differential equation of the family of ellipses having center at the origin and such that the major axis is always equal to 3 times the minor axis and whose directrices are always perpendicular to x - axis. Sketch some of the family of curves.

Q: Find the points on the ellipse x2+2y2=1, where f(x,y)=xy has its extreme values.

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Q: 1. Suppose that the equation Ax + Cy + Dx + Ey + F = 0 represents a conic section (nondegenerative…

A: Fill in the blanks

Q: Refer to Figure 25 in Section 11.5. Prove that the product of theperpendicular distances F1R1 and…

A: Prove that the product of theperpendicular distances F1R1 and F2R2 from the foci to a tangent…

Q: Find the equation of the line tangent to the ellipse x + 3y 19 at the point (4,1). (Type an…

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Q: 1. Find the equation for the parabola that has its vertex at the origin and has directrix at y = 25…

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Q: Identify the conic with th e given equa­tion and give its equation in standard form…

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Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

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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: 5. Eliminate the parameter to find the equation of the ellips Sx(t) = 4 cos(t) + 1 ly(t) = 3 sin(t)…

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Q: Given the general form of all the conic sections: Ax + By + Cx + Dy+ E = 0 Choose what has to be…

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Q: 1. Find the slope and the equation of the tangent line to the curve y=x³ at x=-1 2. Find the slope…

A: Let's find.

Q: Find an equation of a generating curve given the equation of its surface of revolution. x2 + y2 − 2z…

A: Given equation of surface of revolution is, x2+y2-2z=0

Q: Find the point(s) on the hyperbola x^2 - y^2 = 2 closest to the point (0, 1).

A:

Q: 1. Find the maximum and minimum distance from the origin to the ellipse 2² + xy + y² = 3

A: 1) To Find: The maximum and minimum distance from the origin to the ellipse x2+xy+y2=3. As per…

Q: 6. y=x(x-2)(x-) plot the conic Curve

A: Given, y =xx-2x-10  We have to plot the curve.

Q: Example 4: Obtain the differential equation of the family of ellipses whose axes coincide with…

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Q: 4. Find the slope of the curve r = cos 20 at the origin 5. A particle moves along a path whose…

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Q: 1 Find the equation for the parabola that has its vertex at the origin and has directrix at y 27…

A: Given: y=-127.

Q: On a separate piece of paper, sketch the graph of the parabola y = x + 3. On the same graph, plot…

A: Given: Equation of parabola, y=x2+3

Q: The equation x2 - xy + y2  =3 represents a “rotatedellipse,” that is, an ellipse whose axes are not…

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

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Q: If P1 and P2 are two points on the conic whose angles θ1 and θ2 differ by 180° , show that the…

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Q: 4) Find the critical points of the parametric equations x = t* – 1 y = t3 -t

A: Topic:- application of derivatives

Q: 1. Suppose that the equation Ar + Cy + Dx + Ey + F = 0 represents a conic section (nondegenerative…

A: Given: Ax2+Cy2+Dx+Ey+F=0.

Q: 4. Find the equation of the tangent plane at the point (-2, 1, -3) to the ellipsoid 22 + y? + = 3 4

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Q: Two children weighing 16 and 24 kilograms are sitting on opposite sides of a seesaw, both 2 meters…

A: Given,           Two children weighing 16 and 24 kilograms are sitting on opposite sides of a…

Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

Q: (c) (d) Determine the exact length of the curve of the conic section from 0 = 0 to 0 = π/6. Explain…

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Q: Find the largest and smallest outputs of f(x,y)=x2+2y2 on the weird slanted ellipse…

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Q: Find the Differential Equation of the Family of Ellipses with its center at the origin.

A: Here is the solution:

Q: 1. Determine the orthogonal trajectories of the family of ellipses 16x + 121y = c. Sketch some of…

A: Given that equation of ellipses 16x2+121y2=cTo find equation of orthiginal trajectarySolution if…

Q: 64. Find equations of both the tangent lines to the ellipse x² + 4y2 = 36 that pass through the…

A: Given: The Equation of the ellipse is x2 + 4y2 = 36

Q: Find an equation of a generating curve given the equation of its surface of revolution. 8x2 + y2 +…

A: It is required to find the equation of generating curve given the equation of its surface of…

Q: Solve for the Differential equation of the following problem:  All ellipses with center at the…

A: We have to find differential equation

Q: A particle is moving on the curve defined parametrically by the system of equation x = 1- 2cos?t and…

A: Distance of particle from origin is:

Q: (a) The associated parametric curve is one-half of what familar conic? Sketch the exact curve. r (t)…

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question...…

Q: 4. Solve for the critical points of the given parametric equation: x = t³ – 1; y = t² + t

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Q: Find an +y² equation for the tangent to the ellipse 4 = 2 at the point (2,0).

A: Consider the ellipse, x24+y2=2

Q: (x- 2), (y-6)² Problem #4: Find the slope of the line tangent to the conic section =1 at 16 25…

A: This question is related to Straight lines, we will solve it using given information.

Q: Find the equations of the normal and the tangent to the hyperbola xy + 2x - 5y-2= 0 at the point (3,…

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Q: 3. Find equations of both the tangent lines to the ellipse x²+4y?=36 that pass through the point…

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Q: 6. Find the area and centroidal distances of the curve that lies between the equations y-4-x^2 and…

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Q: (41, Ellipse:. x = h + a cos 0, y= k + b sin 8

A: Form ellipse

Q: 1. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch es. %3D

A: Topic = Geometry

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: 15. Find an equation for the ellipse of eccentricity 2 that has the line メニZ as directrix and the…

A: Please refer the attached image for complete solution.

Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

A: Given that a person shoots a basketball overhand from a position 8 feet above the​floor, then the…

Q: Find a generating curve on the xz-plane for the surface of revolution with equation x²+ y²+ z²= e2x

A: Solution: Given equation is x^2+y^2+z^2=e^(2x)

Q: 1) Find the parametric equations of the line that is tangent to circle x² + y² = 25 at point (3, -4)

A: Given, Equation of circle: x2 +y2=25 at a point (3,-4). now, parametric equation of the line is…

Q: (x- 2)² , (y-6)² Problem #4: Find the slope of the line tangent to the conic section =1 at 16 25…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.