The center of the ellipse with the given equation 4(x – 5)2 + 3(y – 4)2 = 48 is

Q: 18. Which of the following is standard form of the equation of an ellipse defined by 25x2 + 16y2 –…

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Q: What is the general form of equation of an ellipse if its center is at (3,-1), a = 4, b = 3 and its…

A: The standard form of an ellipse is [(x – c1)2 / a2 ] + [(y- c2)2 / b2 ] = 1 Where (x, y) –…

Q: Find the largest and smallest values that the function ƒ(x, y) = xy takes on the ellipse x2/8 + y2/2…

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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: 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: The equation of the ellipse that has its center at the origin with focus at (0, 4) and vertex at (0,…

A: The ellipse has its center at the origin with focus at 0,4 and vertex at 0,7

Q: O Does the origin lie inside or outside the ellipse with equation (x – 4) 2 + 4(y - 3) 2 = 4?

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Q: The equation x2-xy+y2=1 describes an ellipse. Find the coordinates (x,y) of all the points on the…

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Q: Here is the equation of a conic section such that the ordered pair (Fx, Fy) corresponds to its focus…

A: Given y2-28x+16y-76=0

Q: 2. Find the equations of all horizontal parabolas whose focus is the center of the ellipse 9a? +17y²…

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

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Q: Find the value of Y for the hyperbola defined by the equation y² – x² = 7 at the point (3, 4). dx2

A: The equation is y2-x2=7. First find the value of dydx as follows.…

Q: Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of…

A: Standard form of an ellipse

Q: +1. Give the coordinates of the center, vertices, covertices, and foci of the ellipse with the given…

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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: 6. Find the center of the ellipse with equation 2x² + 3y² + 8x + 6y - 1 = 0 b. (2, -1) а. (2, 1) с.…

A: We will solve the problem.

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: The equation x2 + xy + y² = 1 determines an below. ellipse in the xy-plane shown

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Q: the graph of the equation +kry + 49y = 7 where k is any positive constant less than 14, is an…

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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 equation of the ellipse whose foci are at (7,3) and ( 21,3),and the length of its major…

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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: Find the equation of the ellipse shown in the graph. y 8- |(0, 6) 4 2 (-2, 0) (2, 0) -8 -6 -4 -2 2 4…

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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: 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: Convert the general equation of the ellipse 3x^2+4y^2-6x-24y+3=0 into standard form and give the…

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Q: 7. Find an equation in standard form for the ellipse with center at (5,7), horizontal major axis of…

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Q: The center of the ellipse with the given equation 4(x – 5)² + 3(y – 4)2 = 48 is %3D (-5, 4) (4, 5) O…

A: Solving the problem by finding the centre in standard form.

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

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Q: Find the points of intersection between the line 4y - 3x + 12 = 0 and the ellipse 9x 2 + 16y 2 =…

A: The line 4y-3x+12=0 And the Ellipse 9x2+16y2=144 We need to find the intersection point of the line…

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: The equation x2- x   y + y 2  = 3  represents a “rotated ellipse,” that is, an ellipse whose axes…

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

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Q: What will be the equation of the ellipse with a center at the origin and passes through the points…

A: Given query is to find the equation of ellipse.

Q: The equation of the ellipse that has a center at (4, 1), a focus at (0, 1), and a vertex at (– 1,…

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Q: 15. Find the standard form of the equation of the ellipse satisfying the following conditions.…

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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 minimum and maximum values of f(x, y) = x2y on the ellipse 4x2 + 9y2 = 36.

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Q: the graph of the equation X+kxy + 49y = 7 where k is any positive constant less than 14, is an…

A: Here comparing given equation with standard equation of graph

Q: Find the equation of the minor axis of the ellipse x² +4 y -8x-8y= 44 Select one: Oy = 1 Oy=3 O None…

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Q: 1. Write the equation of the ellipse with endpoints of the major axis (-11, 0) and (11, 0) and minor…

A: Topic- Conic section

Q: 9x2 - 18x + 4y +8y = 23 defines an ellipse with center ( 1 -1 ). The major axis has length and the…

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Q: 5. What is the standard-form equation of the ellipse shown? -2- x2 1 25 %3D 16 1 %3D x2 25 1 16 O x2…

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Q: Find the focus for the given ellipse. 1.)  x2 + y2 = 9

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

Q: The equation of the shown ellipse is -1 Select one: O a. x? + 16y² – 32y- 15=0 O b. x2 - 2x+…

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Q: 3. Write the equation into the standard form of the equation of the hyperbola: x² – 4xy + y² + 8x +…

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Q: 4. (a) Derive the equation of the ellipse z+=1 b² =1. a

A: We need to derive the equation of an ellipse centered at (0, 0) with foci at (-c ,0) and (c, 0) and…