Reduce each equation to a standard form and describe the curve completely by providing the important aspects of the curve, if: ● CIRCLE - center and radius ● PARABOLA - direction of the opening, vertex, focus, ends of latus rectum, and directrix ● ELLIPSE - center and direction of major axis, vertices/co-vertices (endpoints of the major and minor axes), foci, ends of latera recta, and directrices ● HYPERBOLA - center and direction of transverse axis, vertices/endpoints of the transverse and conjugate axes, foci, ends of latera recta, directrices, and asymptotes. 1)  x^2 + y^2 + 6x + 8y = −9

Q: Identify the family of curves of an ellipse if the foci are located on the y-axis and centre of the…

A: Equation of an ellipse with foci on y axis and center at origin is given by  x2b2+y2a2=1…

Q: 3. One point on a parabola is (-9, 11). The focus of the parabola is (3, 2). 1) Write the equation…

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Q: Part C: Graphing 1. List the key properties of each graph. Use these to create a sketch. Indicate at…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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: to a standard form and describe the curve er and radius irection of the opening vertex focus ends

A: The standard form of the circle is: (x-h)2+(y-k)2=r2

Q: Identify the quadric surface each of the following equations represent and sketch its graph in a…

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Q: Determine the equation for the parabola with the given characteristics: focus at (2,6); directrix at…

A: Parabola

Q: Find the focus of middle point chords of the parabola y² = tax, of whic Subtend a of the parabola.…

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Q: Find an equation of the ellipse that has center (-5, 5), a minor axis of length 6, and a vertex at…

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Q: Reduce the equation to a standard form and describe the curve completely by providing the important…

A: The given equation is 2y2+x+8y-4=0. Rewrite the equation in standard form:…

Q: how to determine the maximum and minimum distance of an ellipse given the major axis=477,736 and…

A: Length of the major axis is 477,736 Length of the minor axis is 477,078 We need to calculate the…

Q: Which quadric surfaces have both hyperbolas and parabolas as traces?

A: Consider the given: The intersection of a three-dimensional surface and a plane is called a trace.…

Q: 4. Find the equation of the ellipse assuming the form + = 1 if distance between foci 4, between…

A: Use simple standard equation

Q: 3. Equation: Center: Vertices: Co-Vertices: Foci:

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Q: 1. Find the equation of a) a circle with center (2,-3) and passes through the point (5,-1). b) the…

A: a) Here given that center of circle is (2,-3). Since circle passes through the point (5,-1). So,…

Q: ind the foci, major & minor vertices, focal diameter, length of the major and minor axes, equations…

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Q: If the focal length of a parabola is 6 units and the vertex is (3, 2), is it possible to determine…

A: Focal length of a parabola is 6 units and the vertex is (3, 2).

Q: If the directrix is horizontal, then the parabola opens (horizontally/vertically).

A: Given:We must find the missing word in the given sentence.So, Definition of parabola said:A parabola…

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

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Q: Given the ellipse : 1 (x+2)² + (−1)² = 9 4 (a) Graph the ellipse, together with its major and minor…

A: The blue dashed line represents the horizontal and vertical lines passing through the center.

Q: a parabola with vertical axis with focus at (2,1) and whose latus rectum has length of 4, find the…

A: The standard form of the parabola with the vertical axis is: (x-h)2=4a(y-k)                ....(1)…

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.