A. 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. B. Draw the graph of the equation. 2y2+x+8y-4=0

Q: . Reduce the general equation of the circle 8x + x2 - 2y + y2 = 64.  2. Determine the opening,…

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Q: Write the standard form of the equation of the circle with the given center and radius. (10, 0); 2

A: Given center (h,k)=(10, 0)  radius, r= 2

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: Question 4 Determine the standard equation of the circle with center at (-5,0) and diameter of 18. A…

A: A circle is a two-dimensional figure. It is represented by the locus of a point whose distance from…

Q: For each curve in Figure 31, state whether it is symmetric with respect to the y-axis, the origin,…

A: To state whether it is symmetric with respect to the y-axis, the origin, both, or neither.

Q: A parabola is the locus of points equidistant from a given point (focus) and a line (directrix).…

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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: =l a

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Q: Determine whether the statement is true or false. If the statement is false, make the necessary…

A: The statement given is ,  The equation of the circle whose centre is at the origin with radius 16 is…

Q: It is true that the vertex is halfway between tje focus and the directrix on the principal axis

A: Yes, the vertex is halfway between focus and the directrix on the principle axis

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: uestion 1: For the graph of the circle below whose equation is of the form (x-h)²+(y-k)² = r2, enter…

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Q: Find an equation of the circle in standard form with center at (1, 5) that is tangent to the x-axis.…

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Q: 5. Find the center and radius of the circle with equation (x + 1)² + (y - 3)² =9. Then graph the…

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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.

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.