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

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

A: Fill in the blanks

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

A:

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

A:

Q: 5. Find the maximum and minimum values f(x, y) = xy can take on the ellipse 4x²+y? = 16.

A: The given function f(x,y)=xy to the ellipse 4x2+y2=16

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

A:

Q: 9. Explain in your own words how to decide what kind of conic it is if you have the equation Ax? +…

A:

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

A:

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: 19. What type of conic section is given by the equation 4x+ 9y = 36? What are its domain and range?…

A: General equation of an ellipse is given by, x2a2+y2b2=1 Domain of a function y=f(x) is the set of…

Q: 5(c) Find the rectangle with the largest area that can be inscribed in the top half of the ellipse ²…

A:

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 the tangent line. To the ellipse x²+4y²=8 parallel to the line x+2y=6

A: Equation of ellipse is , x2+4y2=8Differentiate w.r.t.x2x+8ydydx=0Subtract 2x from both…

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…

A:

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

A:

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

A:

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: 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: 14. Find the maximum and minimum values of the function f(x,y) = xy on the ellipse given %3D by the…

A: Let f(x,y)=xy subject to     g(x,y)=x2+y24-1=0 We want to find extreme values of f(x,y)=xy on the…

Q: 5. An elliptic cone with an ellipse trace parallel to yz-plane, A. Has a hyperbola trace in both xz-…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

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

A:

Q: Find the slope of the line tangent to the conic section 25 (х-2)2 (y-6)2 = 1 at (2,10). 16

A:

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

A:

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: Explain why a cubic Bézier curve is completely determined by x(0), x (0), х(1), and x'(1).

A:

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: Using the traces obtained in IV.1., provide a hand-drawn sketch of S3. Label all important points…

A: The equation of the surface given is as follows: 4x2-9y2=9z2+4 (3) The graph of the traces obtained…

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

A:

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 an equation of the tangent line to the hyperbola defined by (5x^2)+(4xy)−(2y^2)−4x=195 at the…

A:

Q: 1. Determine the orthogonal trajectories of the family of ellipses 16x? + 121y² = c. Sketch some of…

A:

Q: 17. Let f(x, y) xy. Find the minimum and maximum values on the ellipse x² + 4y² = 4.

A:

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

A:

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

A:

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

A: Form ellipse

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

A:

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: (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.