2. Consider the equation of an ellipse given by; (x-4)² (y-2)² 1 36 20 a. Find the coordinate of the center: b. Find the coordinate of the vertices. c. Find the coordinates of the co-vertices: d. Find the coordinate of the foci E Dlot oll the n ints and sketch the graph of the ellipse.

2. Consider the equation of an ellipse given by; (x-4)² (y-2)² 1 36 20 a. Find the coordinate of the center: b. Find the coordinate of the vertices. c. Find the coordinates of the co-vertices: d. Find the coordinate of the foci E Dlot oll the n ints and sketch the graph of the ellipse.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Rational Functions And Conics

Section4.3: Conics

Problem 98E

See similar textbooks

Related questions

Q: 9) For the equation of ellipse below, find center and vertices. * 4y2 + 3(x – 1)² = 24

A: Consider the given equation of the ellipse. 4y2+3x-12=24 Divide by 24 on both the sides of the…

Q: The equation of the ellipse that has its center at the origin with focus at (0, 4) and vertex at (0,…

A: The ellipse has its center at the origin with focus at 0,4 and vertex at 0,7

Q: The equation of the ellipse that has a center at (7, 3), a focus at (4, 3), and a vertex at (12, 3),…

Q: Consider the two ellipses in the x y plane given by the equations (x-1) -1 and (x+2)v- 5) . 22 (a)…

A: given ellipses are (x-1)262+y232=1…

Q: Find the standard form of the equation of the ellipse with the given characteristics. Foci: (0,0),…

A: Since foci lie on y-axis, so the ellipse is of type where (h,k) is center of ellipse and 2a is…

Q: Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of…

A: Standard form of an ellipse

Q: Find the equation of the ellipse with foci and 0, and vertices (0, - 2) and (0,2). O x? y2 1 4 %3! O…

Q: The equation of the ellipse that has a center at (9, 1), a focus at (5, 1), and a vertex at (4, 1),…

Q: Consider the two ellipses in the x y plane given by the equations (x-1)2 2 =1 and (x+2)2 (y-5)2 62…

A: Given: The given ellipse equations are x-1262+y232=1and x+2222+y-5242=1

Q: The equation of the ellipse that has a center at (8, 2), a focus at (12, 2), and a vertex at (3, 2),…

A: Given : An ellipse has a center at (8,2) a focus at (12,2) and a vertex at (3,2).

Q: The equation of the ellipse that has a center at (4, 2), a focus at (7, 2), and a vertex at (9, 2),…

A: We will find the equation of ellipse as shown below

Q: The equation of the ellipse that has a center at (1, 4), a focus at (– 2, 4), and a vertex at (6, 4)…

A: center(1,4) focus(-2,4) vertex(6,4)

Q: b) For the ellipse 9x+ 2y2 18, find the vertices ,foci, semi major and semi minor axes, and sketch.

A: Given: 9x2+2y2=18 Ellipse standard equation x-h2a2+y-k2b2=1 is the ellipse standard…

Q: The ellipse given by the equation 30x^2+5y^2+40y=120x-50 The center is: ? It has foco at: ? and ?…

Q: Determine the standard equation of the ellipse. Vertices at (- 6, - 2) and (0, – 2); focus at (- 1,…

A: From the given data Vertices at (-6 ,-2) and (0,-2) and focus at (-1,-2) We have center equal to…

Q: 47 Find the standard form of the equation of the ellipse with the given char (x – 3)² (y – 2)² = 1 x…

A: Standard form of the ellipse

Q: 14.) Find the center, foci, vertices, and eccentricity of the ellipse, and sketch the graph of (x –…

Q: The following equation is already given in the standard form: (x-4)² (y + 3)² + 1 25 49 Sketch a…

Q: What is the equation of the standard ellipse with vertices at (±a,0) anc Choose the correct answer…

Q: 1. Given the equation of the ellipse, list the coordinates of the center, vertices, co-vertices and…

Q: I. Find the standard equation of the ellipse which satisfies the given conditions. 4. covertices…

A: As per Bartley guidelines we are supposed to answer only one question per post. This post contains…

Q: Given the ellipse (z- 4)2, (y+3)² 144 16 what are the vertices and co-vertices of the ellipse?

Q: Find the coordinates of the foci for the following ellipse (Y+8)²/81 +(x-1)²/49

Q: 2. Consider the equation of an ellipse given by; (x-4)² + 36 (y-2)² 20 a. Find the coordinate of the…

A: This questions based on the geometry.question solve in part 2.

Q: Determine the standard equation of the ellipse that satisfies the given properties: center at the…

Q: Graph the ellipse with the given equation (x-1)² (y+2)² 9. = 1 4 and identify the 1. direction…

Q: The equation of the ellipse that has a center at (8, 5), a focus at (11, 5), and a vertex at (13,…

A: The equation of ellipse is: To find A, B, C, D

Q: The equation of the ellipse that has a center at (9, 2), a focus at (5, 2), and a vertex at (4, 2),…

A: Given Data The centre point is (9,2). The focus point is (5,2). The vertex point is (4,2). The…

Q: (x – 2)2 (y – 4)² 1 9. 25 defines an ellipse with center ( ). The major axis has length and the…

A: The standard form of the equation of an ellipse having vertical major axis is

Q: Which of these is the equation of an ellipse with a minor axis 6 units long and a major axis 14…

A: By using equation of ellipse formula, we find the required equation of ellipse

Q: Determine the standard equation of the ellipse that satisfies the given properties: 16 3, horizontal…

Q: I am needing assistance with the attached equation.

A: Foci = (0,0) and (0,6) So, center of it: Major axis = 12 So, 2a=12 a=6 This ellipse is vertical…

Q: Consider the equation of an ellipse written in terms of x and y as 13 z? + 8 yz + 7 y² = 1 a. Find…

A: Note:- For a non singular square matrix A, A = PT D P Here, P is orthogonal matrix that is, P-1 =…

Q: (x – 4)? (y – 3)? = 1, | Given the ellipse 4 25 Find the center point: List the vertices (separated…

Q: The equation of the ellipse that has a center at (4, 1), a focus at (0, 1), and a vertex at (– 1,…

Q: For the ellipse (x-1)^2/16+(y+3)^2/4=1, find the center, vertices, foci co vertices and…

A: The given ellipse equation is (x-1)^2/16+(y+3)^2/4=1 To find the center, vertices, foci co vertices…

Q: The equation of the ellipse that has a center at (6, 1), a focus at (10, 1), and a vertex at (1, 1),…

Q: 4. Find the equation of ellipse having its center at the origin, focus at (0, 3) and a vertex at…

Q: Find the standard equation of an ELLIPSE with FOCI (3, ±2)and MAJOR axis with length 8. A. + = 1…

Q: The equation of the ellipse that has a center at (8, 5), a focus at (5, 5), and a vertex at (13, 5),…

Q: 13. Find the standard form of the equation of the ellipse satisfying the following conditions: Foci:…

Q: Find the equation of an ellipse with center at (2,-2), vertex at (7,-2) and focus at (4,-2)? O (x +…

A: We have to find the equation of ellipse

Q: (z + 5)², (y – 1)? - Given the ellipse 4 = 1 9. + Find the center point: Give the vertices: Give the…

A: Ellipse with center h, k=-5, 1, b=3, a=2. Ellipse vertices given: -5, 4, -5, -2. Endpoints of the…

Q: The equation of the ellipse that has a center at (7, 3), a focus at (3, 3), and a vertex at (2, 3)…

Q: (x – 2)? (y – 5)? 1 Given the ellipse 16 Find the center point: (2,5) List the major vertices…

A: Given the ellipse x-229+y-5216=1To find the center point.To list the major vertices.

Q: Find an equation of the ellipse with vertices (±4, 0) and foci (+2,0). (A 16 y2 = 1 12 B = 1 16 y2 =…

A: Topic:- ellipse equation

Q: The equation of the ellipse that has a center at (3,5), a focus at (-1,5), and a vertex at (−2,5) is…

A: Given: Equation of ellipse: (x-C)2A2+(y-D)2B2=1 Center: (3, 5) Focus: (-1, 5) Vertex: (-2, 5)

Q: The equation of the ellipse that has a center at (7, 3), a focus at (4, 3), and a vertex at (12, 3),…

Q: Find the center, the vertices, and the foci of the ellipse. Then draw the graph. Choose the correct…

Q: Give the coordinates of the center, vertices, covertices and foci of the ellipse with the given…

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

Solve for the equation of the ellipse. Show all work. (Precalculus 1)

2. Consider the equation of an ellipse given by;
(x-4)²
+
36
(y-2)²
20
a. Find the coordinate of the center:
b. Find the coordinate of the vertices.
c. Find the coordinates of the co-vertices:
d. Find the coordinate of the foci
f. Plot all the points and sketch the graph of the ellipse.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Ellipses$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.