Find the center, vertices, foci, and eccentricity of the ellipse. 9x2 + 4y2 − 36x + 40y − 8 = 0

Q: 3. Find the coordinates of the foci of the ellipse given by the equation 4x² + y? = 64. O (0, 4v3)…

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Q: Find the end points of the minor and major axis for the graph of the ellipse (x – 4)? 25 (y – 6)² 1…

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Q: A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one…

A: The standard form of a hyperboloid of one sheet is, x2a2+y2b2-x2c2=1 The hyperboloid needs to be…

Q: 4. The upper half of the ellipse centered at the origin with axes of length 2a and 2b is described…

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Q: The ellipse (x²/16) + (y²/9) = 1 is shifted k units to generate the ellipse a. Find the foci,…

A: Given: x216+y29=1⇒ a2=16   and  b2=9⇒a=4   and…

Q: Find the center, vertices and foci of the ellipse x? +4 y? - 6 x - 16 y = 39 Select one: O Center =…

A: The standard form of an ellipse whose major axis is parallel to the x-axis is given by  . If then…

Q: Find the vertices, foci, and the lengths of the major and minor axes for the ellipse + = 1. 16…

A: The given equation of ellipse in standard form

Q: Find the center, vertices, foci, and eccentricity of the ellipse. x2 = 1 169 144 center (х, у) 3D…

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

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Q: The plane x + y + 2z = 30 intersects the paraboloid z = x^2 + y^2 in an ellipse. Find the points on…

A: Given the plane x + y + 2z = 30 intersects the paraboloid z = x^2 + y^2 in an ellipse. We need to…

Q: Find the center, vertices, foci, and eccentricity of the ellipse. y2 x2 + 16 121 (x, v) = ( center…

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Q: Find the center and foci of the ellipse. (x+5) (y+9)² = 1 %3D

A: The given ellipse equation,(x+5)25+(y+9)29=1

Q: Find the equation of the vertical ellipse that is centered at ( 16, 24), passes through the point (…

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Q: Find the end points of the minor and major axis for the graph of the ellipse(x−2)^2/25+(y−1)^2/36=1…

A: The general form of ellipse equation is,                                               x-h2a2+y-k2b2…

Q: Find an equation of the ellipse with foci at (−3,7)and (−3,−3) and whose major axis has length 20.…

A: The foci of the ellipse is (−3,7)and (−3,−3). The length of the major axis is 20.

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: The ellipse with semi-major axis a, eccentricity e and foci F1 and F2 intersects the circle with…

A: The principle of ellipse is what we have to use here. a is the semi major axis of an ellipse.  Then…

Q: Find the lengths of the major and minor axes of the ellipse x2 +4 y-6x-40 y=-100 Select one: O…

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Q: I. Directions: ldentify the center of each ellipse. 1. (x+4) 2 16 + (y-3) 24 = 1 Center: 2. (x-4)…

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Q: find the perimeter of the ellipse x2/a2 + y2/b2 = 1.

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Q: A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one…

A: Given a cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of…

Q: Find the equation of the ellipse that has center C (0, 4), foci F1 (0,0) and F, (0, 8), and major…

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

A: topic- ellipse

Q: An ellipse has its major axis on the x-axis, center at ( -3, 0 ), one of the vertices at ( -5, 0 )…

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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: Find an equation of the ellipse drawn below, then find its foci. YA Select one: 1 a. (x²/4)-(y²2/9)…

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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: Which is NOT true about ellipse? O the length of the minor axis is always longer than the major…

A: We need to find which is not true about ellipse In ellipse we have two axis minor axis and major…

Q: Find the coordinates of the foci for the following ellipse (Y+8)²/81 +(x-1)²/49

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Q: Consider the parabola P with equation x^2 = 20 (y - k) and whose directrix has equation y = −7. The…

A: This question is related to conic section , we will use the give conditions to find the equation of…

Q: Find the points on the ellipse 3x2 + y2 = 3 that are farthest away from the point (1, 0). What I…

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Q: Find the center, vertices, foci, and eccentricity of the ellipse. x2 y? 169 144 center (х, у) -…

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Q: Find the center, foci, and vertices of the ellipse. x2 + y + 4)² - 1 25 center (x, y) = focus (х, у)…

A: Given, x29 + (y+4)225 = 1 (x-0)29 + (y+4)225 = 1 It is the standard form of the equation of the…

Q: Find the vertices and foci of the ellipse. x2 + 3y2 + 6x – 18y + 33 = 0 vertices (x, y) = ( 3 – V3,3…

A: x2+3y2+6x-18y+33=0 On simplification, we get…

Q: 4. The base is the ellipse 4> cross section is a semici the x-axis.

A: Given ellipse equation is  4x2+y2=1 Solve for y y2=1-4x2Take square root on both sidesy=1-4x2 The…

Q: Find the lengths of the major and minor axes of the ellipse x2 +4 y2 -8x-32 y =-44 Select one:…

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Q: The length of the major axis of the cllipse with center (-4, 1), minor axis parallel to the y-axis…

A: Equation of ellipse with center (-4,1) is given by

Q: Consider the ellipse x2 + 4y2 = 1 in the xy-plane. a. If this ellipse is revolved about the x-axis,…

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Q: Find the center, vertices, roci, and eccentricity of the ellipse. x2 y² = 1 121 49 center (х, у) %-…

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Q: Find the end points of the minor and major axis for the graph of the ellipse (x – 4)² + (y – 4)² 1 9…

A: The equation of the ellipse                                          x-429+y-4236=1 We have to…

Q: Find the center, foci, and vertices of the ellipse. x² + Sy + 4}² - 1 25 center (x, y) = (0, – 4 (x,…

A: Given: x29+y+4225=1 To determine: Center, foci & vertices of the ellipse. Also, to find length…

Q: A landscape architect is designing an elliptical pool that will fit in the center of a 20-by-30-…

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Q: 9) For the equation of ellipse below, find centre and foci. 4(y+ 1)² + 7(x – 1)² = 28 Centre (-1,1),…

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Q: The ellipse 6x² + 2x + y? = 1 has its center at the point (b, c) where b = c = The length of the…

A: The standard form of an ellipse is with (h,k) as the centre.

Q: ellipse. Use a graphing utility to graph the ellipse. 2x2 + y2 + 7.2x − 7.2y + 9.44 = 0 center…

A: Given query is to find the centre, foci and vertices of ellipse.

Q: Find the end points of the minor and major axis for the graph of the ellipse(x−2)^2/16+(y−4)^2/36=1…

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Q: Find the vertices and foci of the ellipse. x2 + 3y2 + 2x – 6y + 1 = 0 vertices (x, y) = (smaller…

A: Standard form of ellipse x-h2a2+y-k2b2=1 Foci = h±c,k, where c=a2-b2 Vertices = h±a,k

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

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Q: boloid z=x^2+y^2 in an ellipse. Find the points on this ellipse that are nearest to and farthest…

A: In this question, the concept of Lagrange Multiplier is applied. Lagrange Multiplier The Lagrange…

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.