3. Find the coordinates of the foci of the ellipse given by the equation 4x² + y? = 64. O (0, 4v3) and (0, –4v3) | О (, 48) and (0, — 48) О (,4) and (0, —4) O (4/3, 0) and (-4v3, 0)

Q: - Calculate 64x²+16y² dx dy, where D is the interior of the ellipse ()² + (½)² ≤ 1. (Use symbolic…

A: Given,           where D is the interior of the ellipse

Q: x* + 2y? - 2x + 8y - 11 = 0 (illpse) x2 = 1 (llyperholu) 36 64

A: Equation of ellipse given is- x2+2y2-2x+8y-11=0 Standard form of this equation can be written as-…

Q: S52² +32° +22²-32 +2) dz

A: Solving the problem by finding the value of integration.

Q: Graph the conic section 2x² - 12x - y² + 6y+26=0 by completing the square.

A: The given equation is .The aim is to sketch the graph of the conic section.

Q: 5) Find the unique quadratic curve (i.e. parabola) which passes through the following three points:…

A: We have to find the unique quadratic curve which passes through the following points:…

Q: Solve the components of the given equation of conic sections and sketch the graph: а. 9y? — 4x2 +…

A: In this question we have to solve the following question.

Q: Find an equation for the ellipse shown in the figure.

A:

Q: Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8. 1 O f(x) -(x –…

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

Q: 13. Which of the following is the equation of the graph shown? 2 Parabola Oy = - 3x? – 6x – 2 Oy = -…

A: The objective is to find the equation of the graph.

Q: 9. Find the vertex and focus of the parabola whose equation is 24x = -(y – 6)² + 192 O V(-8, –6),…

A:

Q: Find the value of Y for the hyperbola defined by the equation y² – x² = 7 at the point (3, 4). dx2

A: The equation is y2-x2=7. First find the value of dydx as follows.…

Q: 5 Find an equation of the hyperbola having foci at (-2, - 3-/29) and (-2, – 3+ /29) and asymptotes…

A:

Q: Q.9: Classify and find the standard equation of the conic section 4x² +9y² + 36y-16x + 16 = 0, then…

A: Given

Q: The parabola shown in the figure has an equation of the form y = ax² + bx + c -5 y 5 (2, 4), -5 -10…

A: The parabola shown in the figure has an equation of the form .The parabola passes through the points…

Q: Which of the following properties satisfy the parabola with equation x² + 6x + 8y = 7 O v(3,2);…

A:

Q: 1. A parabola has equation -12x + y? – 24 = 0. Write the equation in standard form.

A: The equation of the parabola is, - 12x + y² - 24 = 0 So, y² = 12x + 24

Q: Find the equation for a conic a. Parabola opening left with vertex (3, -1) and passing through (0,…

A: "Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: For which values of a does the conic 3x^2 + 2y^2 − 16y + 12x =a, have at least one point?

A: Consider the given:…

Q: A. Transform each equation to center-radius form and determine its center and radius. 1. x² + y²…

A:

Q: Q2) Put the equation (3x +(y-2) = 3) in standard form and sketch the ellipse.

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

Q: 8. Find the equation of the conic whose focus is (4, -5) and directrix is x = -2.

A:

Q: 10. A comet with a hyperbolic orbit passes within 572,000 miles of the center of the sun with the…

A: Given: A comet with a hyperbolic orbit passes within 572,000 miles of the center of the sun. The sun…

Q: 4) Transform the parabolic equations (9)40xxt120xy けy-20x +0こo x+9 (6) e2x Uxx +2e**Jxy+ e®Uyy=O to…

A:

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

A:

Q: Adjust h, k, and t to reproduce this picture, only with your ellipse being purple instead of green.…

A: Note: According to Bartleby guidelines; for more than one question asked, only the first one is to…

Q: += -5 +2)² + (y+4)² = 1 81 9 =+2)² + (x+4)² 9 81 C-2)² 9 + (y-4)2 81 ation of this ellipse? = = 1 =…

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

Q: 11. Write the equation of the conic section in standard form. 7x² – 3y² – 70x –12y+142 =0

A:

Q: The foci of the ellipse with given equation 25 1 are 36 II +

A:

Q: The vertex of the parabola given by the equation x2 = 20 y is O (0,0) O (4,5) O (0,5) O (4,0)

A: Vertex of the parabola

Q: The center of the ellipse with the given equation 4(x – 5)² + 3(y – 4)2 = 48 is %3D (-5, 4) (4, 5) O…

A: Solving the problem by finding the centre in standard form.

Q: If a parabola y=ax2+ky=ax2+k has vertex (0,−1)(0,−1) and passes through the point (4,2)(4,2). What…

A: A Parabola y=ax2+k       ...(1) has Vertex (0,-1) and Passes through the Point (4,2)

Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

A:

Q: C) (y+2)2=.24(y+2x) D) (x-2)²=-24(y+4) E) (x+2)²=-24(y+2)

A:

Q: The vertices of the ellipse given by = 1 are (2, 1) and (1, 2) (0, 1) and (0, – 1) - O A. В. (-2, 0)…

A: Given:- x2/4+y2/1 = 1 To find:- Vertices of given equation of ellipse

Q: Find the values of integers,, and c that will make the hyperbola -9x² + 4y² + ax +by+c= 0 pass…

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.