14. Evaluate [4x dæ + 5y“ dy if C is the portion of the ellipse 3x2 + 7y? = 21 in the first quadrant, oriented positively.

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A: Except for degenerate cases, the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 defines an ellipse if ____.

Q: x + xy + y? = 9 %3D sa slanted ellipse illustrated in this figure: 1 – 4 -2 2.

A: Given that x2+xy+y2=9 Differentiate w.r.t x , 2x+y+xy'+2yy'=0 y'=-2x+yx+2y Now, differentiate w.r.t.…

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

A:

Q: 27. Find the points on the ellipse 4x? + y? away from the point (1, 0).enigsmuo 4 that are farthest…

A: Given: The equation of ellipse is given as, 4x2+y2=4. The objective is to find the point x,y on the…

Q: Write the equation of an ellipse centered at (1, -2) whose minor axis has length 6 and horizontal…

A: We can find the equation of ellipse using the given data as below.

Q: 8. Give a parametric representation of the given ellipse with the orientation clockwise. x2 y? -=D1…

A:

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

A:

Q: 1- Sketch the following conic sections: y2 -4y+8-4x² = 0 %3D a-. .2 b- .2 y-4y-4x =8 a 3(y – 5)2 –…

A: As per our company guidelines, we are supposed to answer only the first three subparts. Kindly…

Q: Match the ellipsoids shown in the figure above with t 1) x2 + 4y + 4z? = 16 2) 4x2 + y +4z? = 16 3)…

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Q: 4. §yʻ dz + 2ry³ dy, where C is the ellipse z + 2y? = 2.

A: To Determine: find the integral  Given: ∮y4dx+2xy3dy where C is the ellipse x2+2y2=2 Explanation: we…

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: 35. Calculate || 9x*+4y* dx dy, where D is the interior of the ellipse (G) + (4)' =

A: Given:

Q: Find the dimensions of the largest rectangle with sides parallel to the axes that can be inscribed…

A: Let the dimension of such a rectangle be 2x by 2y. Clearly (x, y) is point on the ellipse.

Q: Scalar line integrals Evaluate the following line integral along the curve C.

A:

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: Consider the two ellipses in the x y plane given by the equations (x-1)2 2 =1 and (x+2)2 (y-5)2 62…

A: Given:  The given ellipse equations are x-1262+y232=1and x+2222+y-5242=1

Q: Calculate ne4x+16y° dx dy, where D is the interior of the ellipse

A: Given,            ∫∫De64x2+16y2dxdy where D is the interior of the ellipse x42+y82≤1

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

A:

Q: Q.2. Show that the area of the ellipse =1 is z ab. ab

A:

Q: For which point y on the ellipsoid æ² + 2y² + 4z² =1 (shown below) is %3D the quantity x+ y+ z as…

A: Lagrange's Multiplier:- To find:- Extreme values of f(x, y, z)…

Q: Write the equation of the ellipse 4x + 9y² + 72x + 108y + 612 = 0 in standard form. O (*+9)² +…

A:

Q: #6 57-294x +49x? -160y +16yr =0 write ta enuntion into standared forem of the earvation of ellipse:…

A: Please see the below picture for detailed solution.

Q: What is the equation of the ellipse with the center at (0.0) that passes through the points (2,0),…

A:

Q: 23 +z+1 Evaluate -dz , where C is the ellipse 4x + 9y² = 1. c z² – 3z +2

A: Consider ∫z3+z+1z2-3z+2dz Singularities of this function are the points at which denominator of the…

Q: 3. Find the line normal to the ellipse at X=-1 y= 2+4x-x3

A: Given, y=2+4x-x3 At x= -1 y=2+4-1--13y=2-4+1y=-1 Now point -1,-1

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

A:

Q: 19. The center of the ellipse 4x2 + y2 -16x - 6y – 43 = 0 is at: %3D

A:

Q: Write the equation of the ellipse 4x + 9y + 72x + 108y + 612 = 0 in standard form. O (e+9)² + (y+6)°…

A:

Q: Show that the ellipse 4x + 9y = 45 and the hyperbola x - 4y = 5 are orthogonal %3D

A:

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

A: Given: The equation x2 − xy + y2 = 3 represents a “rotated ellipse”, that is an ellipse whose axes…

Q: Need some help with Greens Theorem and ellipse plz, thanks

A: It is required to calculate the value of the integral using green’s theorem:

Q: F. dr, where C is the ellipse (x + 3)² + 5(y – 2)² = 16 and F(x, y, z) = x²i+ %3D Pj+ z°k.

A: Given: x+32+5y-22=16 Fx,y,z=x2+y2+z2

Q: What is the equation of the ellipse with the center at (0,0) that passes through the points (2,0),…

A:

Q: 4. Evalaute fe xyds, where C is the portion of the ellipse 4 y =1 in the first 16 quadrant, oriented…

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: Find the equation for the ellipse with foci at (-1,3) and (5,3) and whose minor axis has a length of…

A: Given:- The ellipse with foci at (-1,3) and (5,3) and whose minor axis has a length of 4 units. To…

Q: 17. Evaluate F · dš if F(x, y) = (y*, 2xy*) and & is the ellipse x? + 2y? = 2 (with counterclockwise…

A:

Q: Let 49x + 25y 2- 294x - 250y- 159 = 0 (2 – h) (y – k)? = 1. - - then write the ellipse in standard…

A:

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

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Q: Answer the following True or False: (x + 1)² Let (y + 8)? + + 8)? = 1 a2 62 be the equation of an…

A: SOLUTION: (x+1)^2/a^2+(y+8)^2/b^2=1 center=(-1, -8) but in question given center=(1,8) hence false

Q: In the conic section r2 36y, what is the distance between the focus and the center? %3D 0 6 O 12 O…

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Q: 2 %3D what is the eccentricity of the ellipse (x+5)* + l6 y? = 16 ?

A:

Q: I am having trouble solving this.

A: To find the area of the overlap between the interior of the ellipses given below.

Q: Evaluate –dz , where C is the ellipse 4x² + 9y? = 1. %3D Yc z2 – 3z+2

A: Given: The equation: ∮C z3 + z + 1z2 - 3z +2dz Here C - ellipse of 4x2 + 9y2 = 1

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

A:

Q: The ratio of the major axis to the minor axis of the ellipse 9x2 + 4y2 – 24 y – 72x – 144 = 0 is O…

A:

Q: What is the standard equation of an ellipse with center( major axis of length 20 and minor axis of…

A:

Q: Find a parametric description for the ellipse 9x^2+4y^2+24y=0, oriented clockwise and where t=0…

A: Given equation of the ellipse 9x2+4y2+24y=0.

Q: What is the equation of normal to the ellipse 9y^2 + 4x^2 = 25 at (2,-1) ?

A: Slope of normal is -dx/dy  So we differentiate both sides with respect to x Then we plug x=2 and…