Area Find the dimensions of the rectangle of largest area that can be inscribed in the ellipse x2 + 4y2 = 4 with its sides parallel to the coordinate axes. What is the area of the rectangle?

Q: Put the equation of the ellipse in standard form by completing the squqte. 5x2 + 3y2 + 10x + 24y –…

A: This question can be solved using the concept of standard equation of ellipse.

Q: Determine a and b for the ellipse. a= and b= x² — + 2 y. 36 64 =

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Q: Given 4 points on a vertical ellipse (-1.366, 0), (0, 2.241), (1, -12), and (4, 2.43).  Select the…

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Q: The equation of an ellipse centered at the origin is y² = 1, 62 where a and b are distances from the…

A: MATLAB is used as calculator to calculate the results for the algebraic expressions  by typing the…

Q: 6) Complete the square on the ellipse 1622 + 25y? – 32.x + 100y – 284 = 0 to write it in standard…

A: Completing the square on the ellipse 16x2+25y2-32x+100y=284 16x2-32x+25y2+100y=284…

Q: An architect designs two houses that are shaped and positioned like a part of the branches of the…

A: Given Equation:- 2025y2-225x2=455,625

Q: a racetrack is in the shape of an ellipse 100 feet long and 90 feet wide what is the width 10 feet…

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Q: An arch is in the form of a semi-ellipse, with its major axis as the span. If the span is 80 feet…

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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.