1. Give the coordinates of the center, vertices, covertices, and foci of the ellipse with the given equation. x2 a. 169 y2 = 1 144 b. 9x2 + 4y2 = 36 %3D (x-5)2 с. (x+2)2 = 1 49 33 d. 9(x- 3)2 + 16(y-4)2 144 e. 4x2 + 9y2- 40x +36y + 100 0 f. 4x2 + 16x + y2 - 6y- 11 = 0 |

Q: 3. Find the coordinates of the foci of the ellipse given by the equation 4x² + y? = 64. O (0, 4v3)…

A:

Q: What is the length of the minor axis of the ellipse 4x² + 32x + y² – 4y + 52 = 0? 0 4/3 0 4 0 8 O 45

A: Topic = Ellipse

Q: What is the general form of equation of an ellipse if its center is at (3,-1), a = 4, b = 3 and its…

A: The standard form of an ellipse is [(x – c1)2 / a2 ] + [(y- c2)2 / b2 ] = 1 Where (x, y) –…

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),…

A:

Q: B. Determine the center and orientation of the principal axis of each hyperbola. 1. x2 - y2 - 1 4 5…

A: Three equations of hyperbola are given. We have to find the center and orientation of the principal…

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: 5. Find the vertices and foci of the ellipse given by the equation. 4x +9y² - 32x–36y+64=0

A:

Q: Use the properties of an ellipse to show that your equation from question 3 has the appropriate…

A: An ellipse is the set of all points (x,y) in a plane such that the sum of their distances from two…

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

A: Standard form of an ellipse

Q: Which of the following is the reduced equation of the ellipse that has as foci the vertices of the…

A:

Q: +1. Give the coordinates of the center, vertices, covertices, and foci of the ellipse with the given…

A:

Q: 1. Give the coordinates of the center, foci, vertices, and the asymptotes of the hyperbola with the…

A:

Q: Find the dimensions of the largest rectangle with sides parallel to the axes that can be inscribed…

A: Let the dimension of such a rectangle be 2x by 2y. Clearly (x, y) is point on the ellipse.

Q: Given hyperbola   (y + 1)2   −   (x − 2)2   = 1       9                4         what will its…

A: Given: An equation of the hyperbola, y+129-x-224=1.

Q: The equation x2 + xy + y² = 1 determines an below. ellipse in the xy-plane shown

A:

Q: Select the conic section represented by the equation. 5x 2 + 9y 2 - 80x + 54y + 221 = 0 point…

A:

Q: 1. Give the coordinates of the center, foci, vertices, and the asymptotes of the hyperbola with the…

A:

Q: Find the envelope of the family of ellipses defined by the equation x2a2+y2b2=1 provided that…

A:

Q: Find the equation of the ellipse whose foci are at (7,3) and ( 21,3),and the length of its major…

A:

Q: Which of the following is the equation of a vertical ellipse with center (4,6) Major axis 18 and…

A:

Q: What is the equation of the ellipse with the center at (0.0) that passes through the points (2,0),…

A:

Q: The ratio of the major axis to the minor axis of the ellipse 9x2 + 4y2 – 24 y – 72x – 144 = 0 is O…

A: topic- ellipse

Q: 26. Find the standard form of the equation of the specified ellipse. Foci: (1, 5), (-3, 5); Major…

A:

Q: 19. The center of the ellipse 4x2 + y2 -16x - 6y – 43 = 0 is at: %3D

A:

Q: Convert the general equation of the ellipse 3x^2+4y^2-6x-24y+3=0 into standard form and give the…

A:

Q: Select the conic section represented by the equation. 3x 2 + 2x - 5y + 7 = 0 circle hyperbola line…

A:

Q: 7. Write the equation of the ellipse in standard form. 8x +32x + 4y – 8y = -4 (+2)2 4 (y+1)? =1 8 O…

A:

Q: The ratio of the major axis to the minor axis of the ellipse 9x2 + 4y2 – 24 y – 72x – 144 = 0 is %3D…

A: Solution is here

Q: Show that the ellipse 4x + 9y = 45 and the hyperbola x - 4y = 5 are orthogonal %3D

A:

Q: What is the general form of equation of an ellipse if its center is at (3, 1), a = 4, b = 3 and its…

A:

Q: 1. Give the coordinates of the foci, vertices and covertices of the ellipse with equation 169 x2 y²…

A:

Q: Consider the parabola P with equation x^2 = 20 (y - k) and whose directrix has equation y = −7. The…

A: This question is related to conic section , we will use the give conditions to find the equation of…

Q: What is the equation of the ellipse with the center at (0,0) that passes through the points (2,0),…

A:

Q: Select the conic section represented by the equation. 16x 2 - 9y 2 + 64x + 18y - 89 = 0 circle…

A:

Q: What will be the equation of the ellipse with a center at the origin and passes through the points…

A: Given query is to find the equation of ellipse.

Q: Find the equation of the ellipse whose foci are at (2,1 ) and ( 6,1),and the length of its major…

A:

Q: 15. Find the standard form of the equation of the ellipse satisfying the following conditions.…

A:

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

A:

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

A:

Q: (a) Find and identify the traces of the quadratic surface x2 +y2 -z2 =1 and explain why the graph…

A:

Q: Identify the general equation, as well as the coordinates of the foci of the following ellipse that…

A:

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: 5. What is the general form of an ellipse with foci at (0, +2), and vertices at (0, ±4)? 2x + 4y = 0…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the focus for the given ellipse. 1.)  x2 + y2 = 9

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The ratio of the major axis to the minor axis of the ellipse 9x2 + 4y2 – 24 y – 72x – 144 = 0 is O…

A:

Q: Given the ellipse 16x2 + 25y2 – 64x – 50y – 311 = 0, determine its center.

A:

Q: The ellipse 15x^2+2x+y^2=1 has its center at the point (b,c) where b = c=

A: To find the center at the point b, c of the ellipse,15x2+2x+y2=1b=?c=?

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

A:

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.