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

Q: Write the equation of the hyperbola 25x? – 9y? + 100x + 72y – 269 = 0 in standard form (z – h)? (y –…

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Q: Write the equation of the hyperbola 9x² - 36y2 - 18x144y - 459 = 0 in standard form (x - h)² (y -…

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Q: (2+1)- (y-2)" Find the foci of the ellipse. 1 %3D 25

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Q: Write the equation of the ellipse in standard rectangular form that has foci at ( 2 , − 2 ) a n d (…

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Q: (b) Find an equation for the parabola that has axis x = -1 and passes [3] through the points (4,5)…

A: Directrix is a line which together with a point called the focus defines the set of points that form…

Q: Consider the ellipse A. (-5,1) (x-5)² 256 (y-7)² 400 B. (-5,-1) 1. One of the foci is at (-5,15). At…

A: Given equation:- x-52256+y-72400=1

Q: Express the equation of an ellipse 16x² +9y² – 64x-54y+1=0 in standard form. Hence, find the centre,…

A: The standard form of equation of ellipse is x-x02a2+y-y02b2=1 and eccentricity of ellipse is…

Q: 0 = 3x2 – 6x+4y² – 16y+18 is an ellipse. True False

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Q: the ellipse with the given equation is centered at ______. x^2 + 9y^2 + 3x - 18y + 9 a. (3/2,1)…

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Q: Find the points on the ellipse  (x2/9) + y2 = 1 closest to the point (2, 0).

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Q: Sketch and identify the graph of the equation x² + y² – 2y – 3 = 0 in 3D.

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Q: f the equation (5x - 1)² + (5y - 2)² = (y²-2y+1) (3x + 4y - 1)² represents an ellipse then find…

A: Introduction: An ellipse is the locus of all those points in a plane such that the sum of their…

Q: Is the student's analysis correct? Why or why not? Select all correct statements. The analysis is…

A: This is in fact a hyperboloid of two sheets.The standard equation of which is given by .Now the…

Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: Graph the hyperbola (y+3)2/16-(x+6)2/4=1

A: The given equation is (y+3)2/16-(x+6)2/4=1.

Q: Illustrate the coordinates of an ellipse  passing through (h,k) show your complete solution  (…

A: Given information: The equation of the ellipse is (x-3)24+(y+1)29=1. Concept Used: The general…

Q: Graph the hyperbola given by ײ - y² - 72x – 4y +131 - 0.

A: We will graph the hyperbola as shown below

Q: Write the equation of the hyperbola 9x² – 4y? – 54x + 32y – 19 = 0 in standard form (x – h)? (y –…

A: Write the equation of the hyperbola  9x2 - 4y2 -54x +32 y  -19 =0 In the standard form  (x-h)2 /a2 -…

Q: Q2) Put the equation (3x2 + (y – 2)2 = 3) in standard form and sketch the ellipse

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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.