1. Determine the orthogonal trajectories of the family of ellipses 16x² + 121y? = c. Sketch some of the curves.

Q: Show that when a satellite is in elliptical orbit, its speed V is given by v² = k = k ( ² − ²) and…

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Q: Find the equations of both the tangent lines to the ellipse x^2 +3y^2 = 9 that passes through the…

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Q: Find the equation of the line tangent to the hyperbola x + 2xy - y + x = 5 at the point (3,7)

A: Given,            x2+2xy -y2+x =5 and point (3,7)

Q: Find equations of both the tangent lines to the ellipse x2 + 4y 36 that pass through the point (12,…

A: see below the calculation and answer

Q: Find the points on the ellipse 2x + 4y = 1 where f(x.y) = xy has its extreme values.

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Q: Find the maximum and minimum values of the function f(, y) = xy on the ellipse given y? by the…

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Q: Find the points on the ellipse 4x + y² = 4 that are farthest away from the point (1, 0). (х, у) %3D…

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Q: 3. Determine the orthogonal trajectory of the family of parabolas x² – y + 32x = 0. %3D Sketch some…

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Q: B) Use Lagrange multipliers to find the points on the ellipse 2x2+y? = 1, where f (r, y) = ry has…

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Q: The graph of x+6xy+ 25y = 16 is an ellipse. Find the coordinates of the points where the ellipse has…

A: see below the answer

Q: Determine the orthogonal trajectories of the family of ellipses 16x² + 121y² = C. Sketch some of the…

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Q: Find the envelope of the family of ellipses defined by the equation x2/a2+y2/b2=1 provided that…

A: The equation of the family of ellipses is given by provided that  So, the equation of family of…

Q: Find the envelope of the family of ellipses defined by the equation x2a2+y2b2=1 provided that…

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Q: Find the points on the ellipse  X^2 + 6y^2 + 3xy =40 With the greatest x coordinator

A: Let us assume thatfx,y=xandgx,y=x2+6y2+3xy-40The lagrange multiplier equations…

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: 2. Determine the orthogonal trajectory of the family of hyperbolas y? – 121x? = c. Sketch some of…

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Q: The parabola y2 =-14x has it's focus at the point (b,0) where b is?

A: The standard equation of parabola for this condition is y2=-4ax here  Focus (-a, 0)   Now, we have…

Q: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given by the…

A: We have the given function is f(x,y)=xy    ..... (1)   The equation of ellipse  x2+y24=1 Let…

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 points on the ellipse x^2 + 9y^2 = 9 and the line x + y = 10 that are closest and farthest…

A: Distance between the two points: - The length of the line segment connecting two places is called…

Q: Find the equation of the line tangent to the hyperbola x2 −y2 =16 at (5,3).   Give your answer in…

A: The line is tangent to the given hyperbola at (5,3).Tangent line is a straight line.Therefore, the…

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

A: Given :  The function f ( x, y ) = x y and the ellipse  x2 + y24 = 1.   To determine :  The maximum…

Q: Find the point on the ellipse x2 + 6y² + 3xy = 40 with the largest x-coordinate (Figure ). -8 FIGURE…

A: Given: x2+6y2+3xy=40

Q: 14. Evaluate [4x dæ + 5y“ dy if C is the portion of the ellipse 3x2 + 7y? = 21 in the first…

A: Explanation of the solution is given below....

Q: Find equations of both the tangent lines to the ellipse  x2 + 7y2 = 63  that pass through the point…

A: consider (x0 ,y0) be an any point on ellipse

Q: Find the point (x, y) on the ellipse, 4(x - 1)^2+ y^2 = 1, that is farthest to the origin (0, 0).

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Q: Compute the length of the latus rectum of the ellipse x2 + 2y2 +4x+ 4y +4=0

A: Given:    x2 + 2y2 +4x+ 4y +4=0

Q: Find an equation of the ellipse having a major axis of length 12 and foci at (0, 5) and (0, 1). =D ?

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Q: FInd the equations of the tangents with slope m=-2/9 to the ellipse 4x^2+9y^2=40

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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: |The length of the latus rectum of the ellipse defined by 25x²+9y² – 300x – 144 y + 1251 = 0 is А.…

A: To find  The length of the latus rectum of the given ellipse.

Q: 2. Determine the orthogonal trajectory of the family of hyperbolas y² – 121x² = c. c. Sketch some of…

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Q: A large racetrack can be modeled by the ellipse x² + y2 1, where x and y are 4 measured in…

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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: Find an equation of the ellipse with foci at (-5,9) and (-5,-10) and whose major axis has length 22.…

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

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Q: Find the maximum and minimum values of f(x, y) = 7x + y on the ellipse x2 + 9y² = 1

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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: It has been shown that when like particles with a common charge are hurled at each other, they…

A: Let's find.

Q: 1. Determine the orthogonal trajectories of the family of ellipses 16x² + 121y² = c. Sketch some of…

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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. Show that if m is any real number, then there are exactly two lines of slope m that are tangent…

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Q: Find the envelope of the family of ellipses x2/a2+y2/b2=1 having the same area.

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Q: 3 Show thet the ellipse x +3y -) interseet of right ongle T= R_x yjogady puo

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Q: Find the orthogonal trajectory for the family of parabolas with center at the origin and focion on…

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Q: Which is the equation of an ellipse with direcrices at x = =-4 and foci at (2,0) and (-2,0)

A: Center is the midpoint of the foci  midpoint of (2,0) and (-2,0) is : Directrix = -4

Q: Find the point(s) on the ellipse 4x² + y² = 4 that are farthest from the point (1,0).

A: We need to find the points on the ellipse that is farthest from the given point. According to first…