5) a) Show that the point (1,2/2) lies on a circle whose center is the origin and contains the point (0,3). b) Graph the ellipse given by each equation. Find center, foci, vertices and co-vertices, eccentricity, directrix. 4x? +16y² +8x – 64y + 4 = 0

Q: 1.0 1,0

A: Solution attached below

Q: 3) Foci: (-4, -8 + 4√2), (-4, −8 - 4√2) Endpoints of major axis: (-4, -2), (-4, -14)

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Q: Determine if the equation below describes an ellipse and, if so, give its correct center, foci, and…

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Q: 9) Major axis is horizontal Center: (5, -8) Major axis is 24 units long Minor axis is 16 units long

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Q: 27) Foci: (10, 13), (10,7) Endpoints of minor axis: (14, 10), (6, 10)

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Q: Write an equation for each ellipse with the given information.

A: By the geometry of ellipse, and the relationship between lengths of major, minor axes and distance…

Q: Write the equation of the ellipse that has a center at (- 4, - 5), a focus at (– 1, – 5), and a…

A: The general equation of an ellipse centered at a point (h,k) with major axis parallel to the x axis…

Q: Find the standard form of the equation of the ellipse with the give characteristics. Center: (2,6);…

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Q: Graph the ellipse given by each equation. Find center, foci (focus), vertices, co-vertices. a) 4x² +…

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Q: 10) Eccentricity = V119 12 Center: (6,9) Focus: (6-√119,9)

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Q: graph using ellipse center, center axes intercepts (endpoints) and additional points calculated from…

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Q: 23) Foci: (-5, 13), (-5, 7) Endpoints of major axis: (-5, 15), (-5,5)

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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.