2. Find the general equation of the ellipse that shares a vertex and a focus with the paraboladefined by y2 – 4x - 2y + 9 = 0 and whose other vertex is at (12, 1). Draw the conics.3. Find the equation of the plane perpendicular to the plane x – 2y + 3z = 11 and passingthrough the points P(-1,4,2) and Q(3,3,1).4. Draw the polar curve defined by r = 3 – 2 sin 30.5. Convert the polar equation to rectangular form. Simplify your answerp?sec3e = r?tan20 sec e- 4rcsc20

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Find the general equation of the ellipse that shares a vertex and a focus with the parabola defined by y2 – 4x – 2y + 9 = 0 and whose other vertex is at (12, 1). Draw the conics.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Concept explainers

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.

Question

2. Find the general equation of the ellipse that shares a vertex and a focus with the parabola
defined by y2 – 4x - 2y + 9 = 0 and whose other vertex is at (12, 1). Draw the conics.
3. Find the equation of the plane perpendicular to the plane x – 2y + 3z = 11 and passing
through the points P(-1,4,2) and Q(3,3,1).
4. Draw the polar curve defined by r = 3 – 2 sin 30.
5. Convert the polar equation to rectangular form. Simplify your answer
p?sec3e = r?tan20 sec e- 4rcsc20

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