Find the length of major axis of the ellipse x^2+4y^2-2x-8y+1=0

Q: Find the length of latus rectum of the ellipse 36x2 +25v²+72x-50y-839 = 0: Round off your answer to…

A: The given ellipse equation is 36x2+25y2+72x-50y-839=0. First write the equation in standard form as…

Q: What point on the parabola y=3−x2 is closest to the point ​(3​,3​)?

A: Basic differentiation is required.

Q: Find the coordinates of the vertices of the ellipse with foci at (-6,-3) and (10,-3) and has minor…

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Q: Create the equation of a parabola passing through the points (-2,32), (1,5) and (3,17)

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Q: Find the dimensions of the rectangle of maximum area, with sides parallel to the coordinate axes,…

A: Let 2x and 2y be the length and width of rectangle with sides parallel to the coordinate axes, that…

Q: Find an equation of the ellipse that has center (-2, 3), a minor axis of length 10, and a vertex at…

A: Center=(h,k)=(-2,3) Length of minor axis= 2b=10 b=5    a= distance from center to vertex= distance…

Q: What is the general equation of a parabola that opens upward with V(-1,2)?

A: The general equation of the parabola opening upwards is x-h2=4py-k where (h,k) is vertex. here…

Q: Find lengths of minor and major axis for ellipse that has equation 16x2 + 4y2 = 16

A: Given, 16x2 + 4y2 = 16

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

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

A: Given 4x^2 + y^2 = 4 y^2 = 4 – 4x^2 y = +- (4 – 4x^2)^1/2 Let distance between (x,y) and point…

Q: Write the equation of the hyperbola that has a center at (2, – 4), a focus at ( – 2, – 4), and a…

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

A: Let (x,y) is the farthest point on the ellipse from (1,0) Distance between (x,y) and (1,0) is:…

Q: What is the standard form equation of an ellipse that has vertices (6,−1) and (−2,−1) and…

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Q: Find the point on the ellipse 4x2ty3=4 that are farthest away from the point (1,0) 4x27y2-4

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Q: What is the equation of the directrix of the parabola having a vertex at (6,0), passing through…

A: Given:- What is the equation of the directrix of the parabola having a vertex at (6,0), passing…

Q: Can you do a parabola with the starting point being (0,0)

A: Given a parabola with equation y=x2

Q: Give 3 points that lie on the parabola y=x^2-5x-2

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Q: What is the equation of the hyperbola with vertices at (-3,0) and (3,0) and whose conjugate axis has…

A: Hyperbola A hyperbola is a locus of points in such a way that the distance to each focus is a…

Q: Find an equation of the ellipse that has center (3, -4), a major axis of length 4, and endpoint of…

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Q: What is the equation of parabola in standard form whose focus is at (-4,0) and the directrix is at…

A: Note that, the equation of the parabola with the directrix x+a=0 and the focus (a,0) is y2=4ax.

Q: Find the equation of the parabola with vertex (−3,1)(−3,1) and yy-intercept 22(or (0,2)(0,2)).

A: topic - equation of a parabola

Q: Find the larger dimension of this rectangle. If a rectangle of maximum perimeter is to be inscibed…

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Q: What point on the parabola y=(6−x)2 is closest to the point (6​,6​)?

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Q: Find the length, breadth of the rectangular box of maximum area that can be inscribed in the ellipse…

A: The area of a rectangle is Area=Length × Breadth The area is maximum if the second derivative of…

Q: A stationary artist intends to make rectangular cut-outs from the elliptical cardboard that he has.…

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Q: Find the point(s) of intersection of the parabola with equation y = x2 - 5x + 4 and the line with…

A: Given equations are,

Q: Find an equation of the ellipse that has center (4, -4), a major axis of length 8, and endpoint of…

A: Given that: Centre of ellipse =(4, -4)Major axis, 2a=8End point of minor axis = (7, -4)

Q: What is the standard form equation of an ellipse with the center (-1, 6), a horizontal major axis…

A: Center (h,k) = (-1,6) a = 22 b = 8

Q: What are the coordinates of the end points of the latus rectum of the parabola with equation a - 2z…

A: What are the coordinates of the end points of the latus rectum of the parabola with equation…

Q: Find the points on the ellipse 3x + y = 3 that are farthest away from the point (1, 0). smaller…

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Q: What is the length of the conjugate axis of the hyperbola (x^(2))/(16)-(y^(2))/(4)=1?

A: General form of hyperbola   x2a2-y2b2=1  Therefore the length of the Conjugate axis =2b…

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

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Q: Find an equation of the ellipse that has center (4, -4), a major axis of length 8, and endpoint of…

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Q: What is the maximum area of a rectangle inscribed in the ellipse defined by x2/64 + y2/25 = 1? Enter…

A: Let the length and breadth of the rectangle as x, y respectively Area of rectangle = xy Now…

Q: Find an equation of the ellipse that has center (4, -4), a major axis of length 8, and endpoint of…

A: We need to find equation of ellipse.

Q: Write the equation of hyperbola that pass through point (12, 9) and have F1 (0, 0) and F2 (0, 4)

A: Since you have posted multiple question but according to guidelines, we will solve first question…

Q: Find the points on the ellipse 5x2 + y2 = 5 that are farthest away from the point (1, 0). smaller…

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

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Q: What is the equation of the parabola with vertex (1, –11) and that passes through (–4, 64)?

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Q: what is the length of the minor axis of the ellipse 5(x+2)2+(y-0.1)2=125?

A: Given5x+22+y−0.12=125

Q: Find the coordinates of the vertices of the ellipse with foci at (-6,-3) and (10,-3) and has minor…

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Q: Find an equation of the hyperbola having foci at (-2, 6) and (-2, 12) and vertices at (-2, 8) (-2,…

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Q: Find the equation of the ellipse with the major axis from (-9,2) to (1,2) and minor axis from (1,-1)…

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Q: Find the dimensions of the rectangle with maximum perimeter that can be inscribed with sides…

A: Assume the length of rectangle be 2x and width of the rectangle be 2y. Therefore, the perimeter is…

Q: Find the points on the ellipse 3x² + y“ = 3 that are farthest away from the point (1, 0).

A: For the Given Ellipse 3X2+y2=3 ,Points that are  Farthest away from the point (1,0) is calculated as…

Q: Find the maximum area of a rectangle inscribed in an ellipse whose equation is 4x2 + 25y2 = 100.

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Q: What is the standard form equation of an ellipse that has vertices (−2,14) and (−2,−12) and…

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Q: 2- Write the equation of hyperbola that pass through point (12, 9) and have F, (0, 0) and F2 (0, 4).

A: Since, the foci of the given hyperbola are F′(0,0​) and F(0,4​) which lie on the X-axis and…

Q: what is the equation of a horizontal ellipse centered at the point (9,4) whose major axis is 22…

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Q: Find an equation of the ellipse that has center (-5, 3), a minor axis of length 4, and a vertex at…

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