What is the DE of the family of parabolas having their vertices at the origin and their foci on the y- axis? A 2xdx — у dy %3Dо B y dx + x dy = 0 y dx — 2х dy %3D0 (D 2y dx — х dу %3D 0

Q: 5. Calculate the area of a regular hexagon inscribed in a circle of radius 1 unit. a. 1.316 units b.…

A: Area of equilateral triangle = 34 a2 ; where , 'a' is the sides . Note : As per our Guidelines , we…

Q: The part of the hyperboloid 4x 2 - 4y2 - z2 =4 that lies in front of the yz-plane

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Q: Compute the length of the latus rectum of the parabola y2 + 8x – 6y + 25 = 0.

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Q: Derive the equation of the parabola with a focus at (-7, 5) and a directrix of y = -11. O (x)= (X +…

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Q: 2. Which equation represents the parabola with focus (1, 4) and latus rectum of 4? Oy = 4(a- 1)2 + 3…

A: Here, the parabola is of the form (x-h)2=4a(y-k) Whose focus is given by (h,k+a)=(1,4) given…

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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

Q: In the xy-plane, if the parabola with equation y = ax² + bx + c, where a, b, and c are constants,…

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Q: Cоmрute (x + y) dz, where is the portion of the parabola C y = 4 – x2 from -2 to 1+3i.

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Q: 4.The parabola opens O A. upward O B. forward O C. backward O D. downward

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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: What is the equation of a parabola in standard form with vertex V(3, – 3) and focus F(3, 2)? A (x-…

A: NOTE: Refresh your page if you can't see any equations. . the vertex is at  and the focus is at

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: Find the greatest and smallest values that the function f(x,y) = 4xy takes on the ellipse x +2y² = 1…

A: Let's find.

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

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Q: Show that the number 4p is the width of the parabola x2 = 4py (p>0) at the focus by showing that…

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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: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: 1. Find the minimum and maximum values of f(x,y) : = x²y on the ellipse 4x? + 9y? = 36. %3D

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Q: Given hyperbola   x2   −   y2   = 1   9         16       how do you determine the focal length?

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Q: Find the equation of the tangent to the hyperbola x² – 3y² = 1 at the point S(2,-1). A) 2x + 3y – 1…

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Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: How far from the x axis is the focus of the hyperbola (x^2)- (2y^2) + 4x + 4y+ 4 = 0?

A: the given equation of hyperbola is  x2- 2y2+4x+ 4y + 4 =0 it is asked to find how far is focus of…

Q: 4) Consider the images of the hyperbolas r - y = ±c? under the mapping f(2) = 22, where c > 0. Show…

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Q: For each of the following quadratic equations in x and y, determine which conic section it is.…

A: Let Ax2+Bxy+Cy2+Dx+Ey+F=0 is a quadratic equation.Parabola: If B2-4AC =0 AND A=0 OR C=0Circle: If…

Q: Show that the line b2xx1 - a2yy1 - a2b2 = 0 is tangent to the hyperbola b2x2 - a2y2 - a2b2 = 0 at…

A: Find dy/dx.Then find dy/dx at the point (x1,y1) by plugging x=x1 and y=y1

Q: Show that the ellipse x*/a? + y*/b? = 1 and the hyperbola x/A? – y/B² = 1 are orthogonal…

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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: Find the extreme values of f(x, y) = e¬¤y for the points on the ellipse x² + 4y? = 1

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Q: Find an equation of the parabola deseribed. Focus at (5, 0); vertex at (0, 0) O y = 20x2 O x = 20y O…

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Q: Fid the equation of the tanget to the parabola  x2 - 22x + 24y +169 = 0 at  the point whose focus…

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Q: The value of y dæ – x dy where C is the portion of the parabola y = x² – 1 from (0, –1) to (-2, 3)…

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Q: Compute the angle between the asymptotes of the hyperbola 5y² - 4x² + 40y + 60 = 0 Select one: O a.…

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Q: What are the asymptotes of the hyperbola 9æ? – 4y? – 18æ + 24y + 9 = 0 O (y – 3) = +(x – 1) ㅇ (y-3)…

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Q: 28. Find the directrix for the parabola. (y+ 3)2 + 8 2x x = 4 y = } 7/2

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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: Evaluate x° ds where C is the part of the parabola y = x² from (0,0) to (2, 4).

A: Form the double integral and set the limits than integrate with respect to y and x.

Q: The hyperbola with vertices at (0, 3) and (0, – 3) and foci at (0, 5) and (0, – 5) has the equation…

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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: Find the equation of the hyperbola that is centered at (0,0), has vertices at (t10,0) and has 6.…

A: Consider the given values. Center=0,0vertices=±10,0y=±65x The gerneral equation of hyperbola with…

Q: 4x2 dx - xy dy 16x2, y = o from (-1, 0, 16) to (1, 0, 16) (d) dz, where c is the parabola z

A: To evaluate the line integral along the arc C of the given parabola

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A: Vertices of parabolas = (0,0), Foci on the y-axis.

Q: What is the equation of the directrix of a parabola having vertex at (4, 3) and focus which is 2…

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Q: A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating…

A: Let's find how far from the vertex should the bulb be placed.

Q: The area of the region to the left of the parabola x=2y^2, to the right of the y-axis, and between…

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Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: Find the equation of the Hyperbola whose Foci are at (2,1) and ( 10,1),and the length of its…

A: Given: Foci ≡ 2,1 and 10,1, Length of the Transverse axis = 4

Q: Which is the equation of a parabola with a directrix at y = 2 and a focus at (5, 0).

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