Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (−1, 0).

Q: Find the length of latus rectum of the ellipse 36x2 +25v²+72x-50y-839 = 0: Round off your answer to…

A: The given ellipse equation is 36x2+25y2+72x-50y-839=0. First write the equation in standard form as…

Q: Find the standard equation of the hyperbola. Two corners of auxiliary rectangle at (−4 ,−7) and (0…

A: Given: The two corners of the auxiliary rectangle of a hyperbola are at -4,-7 and 0,0 and transverse…

Q: Find an equation for parabola with vertex  (−1,3) and directrix x=−4.

A:

Q: Find the coordinates of the vertices of the ellipse with foci at (-6,-3) and (10,-3) and has minor…

A:

Q: Which point on the graph of the parabola y= 4x2 has the minimum distance between the graph and the…

A: To solve this question find a function in 'x' using the distance formula equate the derivative of…

Q: Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0). (x, y) =…

A: We have to find the point which is farthest away from the point 1,0 at the ellipse: 4x2+y2=4 Writing…

Q: Find the dimensions of the rectangle of maximum area, with sides parallel to the coordinate axes,…

A: Let 2x and 2y be the length and width of rectangle with sides parallel to the coordinate axes, that…

Q: Find the points on the ellipse 4x + y² = 4 that are farthest away from the point (1, 0). (х, у) %3D…

A:

Q: Find the equation of parabola “y = ax2 + bx + c” passing through points (1, -6), (2, -3), (-1, 0)

A: Consider the given points and the equation of the parabola. Obtain the system of equations with a, b…

Q: Find the equation of the parabola with vertex (−3,1) and y-intercept 2(or (0,2)).

A: We have to find the equation of the parabola with vertex (−3,1) and y-intercept (0,2).

Q: Find the equation of the parabola in standard form vertex at the origin passing through the point…

A:

Q: Find the slope of the ellipse x2 + 4y2 -10x - 16y +5=0 at the point where y=2 + 80.5 and x=7

A:

Q: Find the equation of the parabola with vertex (2, 4) and directrix x = –3

A: Given: Vertex (2,4)

Q: Find the points on the ellipse 3x + y = 3 that are farthest away from the point (1, 0). %3D smaller…

A:

Q: . What is the snortest distance between the parabola y=2x² and the line y=4x-4

A: Shortest distance between two curves are always along the common normal.

Q: What is the equation of the parabola which has vertex (1,2) and y-intercept y = 1?

A: See the details solution in below

Q: What is the equation of the parabola with axis parallel to the x-axis, whose vertex is at (-1,7) and…

A:

Q: Find the equation of the parabola and put it in the form f(x)= ax^2 +bx+c  Given:  vertex: (7, -4)…

A: Explained below

Q: Find the points on the ellipse 5x2 + y2 = 5 that are farthest away from the point (1, 0).   smaller…

A:

Q: Find an equation of the parabola with vertex (-1,3) and directrix y=7 .

A:

Q: A point moves on the parabola y2 = 8 in such a way that the rate of change of the ordinate is always…

A: The given parabolic curve is, y2 = 8x    ...(1)   It is given that the rate of change of ordinate is…

Q: Find the equation of the plane through the points (0, 1, 1), (1, 0, 1), (1, 1, 0) Thank you.

A:

Q: What is the equation of the parabola that has a max of (2,3), and passes through point (, -1)?

A:

Q: Can you do a parabola with the starting point being (0,0)

A: Given a parabola with equation y=x2

Q: What is the equation of the hyperbola with vertices at (-3,0) and (3,0) and whose conjugate axis has…

A: Hyperbola A hyperbola is a locus of points in such a way that the distance to each focus is a…

Q: Find the equation of the parabola that goes through the points (-2,16), (-1,6), and (2, 12).

A:

Q: Find the equation of the parabola with vertex (−3,1)(−3,1) and yy-intercept 22(or (0,2)(0,2)).

A: topic - equation of a parabola

Q: Find an equation of the parabola with vertex (3, 4) and directrix y = 1.

A: Graph of parabola :

Q: Find the larger dimension of this rectangle. If a rectangle of maximum perimeter is to be inscibed…

A:

Q: Determine the equation of the parabola with vertex (2,8) and x-intercepts 0 and 4 in factored form…

A:

Q: Find the equation of the parabola whose axis is vertical and passes through (-1,0), (5,0) and (1,8).

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

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: Classify the conic section of each equation.  Explain how you made your decision. 13. 4x2 + 3x = y2…

A: Topic = Conic section   The equation of every conic can be written in the following form:   Ax2 +…

Q: Find the length of the diameter of the ellipse 3x2+y2 +2x-6y=0. Which has a slope of 2.

A: Ellipse

Q: Find an equation of the parabola with vertex (-5,-4) and directrx y =-11,

A:

Q: Find the point on the ellipse x2 + 3y + 2xy = 6 with the greatest x-coordinate. (Use decimal…

A:

Q: Find an eguation of the sphere that passes through the point (5,-2,-1) whose whose Center is the…

A:

Q: Find the points of intersection of the parabola with equation 2x + y² + 4y – 2 = 0 and the line…

A: Here we find the intersecting point of parabola and the line.

Q: What is the equation of the parabola with vertex (1, –11) and that passes through (–4, 64)?

A:

Q: ress 3x² + y² + 2z² + 6x – 4y

A: Given,            3x2+y2+2z2+6x-4y-12z+26=0

Q: What point on the parabola y = 3- x² is closest to the point (3,3)? The point on the parabola y = 3…

A:

Q: Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0). (x, y) =…

A:

Q: Find the dimensions of the rectangle with maximum perimeter that can be inscribed with sides…

A: Assume the length of rectangle be 2x and width of the rectangle be 2y. Therefore, the perimeter is…

Q: The equation of the sphere with center (7,-10, 1) that touches that y-axis is

A: To find the equation of the sphere we need center of the sphere  radius of the sphere.  Here given…

Q: 2- Write the equation of hyperbola that pass through point (12, 9) and have F, (0, 0) and F2 (0, 4).

A: Since, the foci of the given hyperbola are F′(0,0​) and F(0,4​) which lie on the X-axis and…

Q: Find the equation of the parabola with directrix x + 2 = 0, axis y = 4, and latus rectum 4.

A:

Q: 4x^2 + y^2 = 4 that are the farthest away from point (1,0)

A:

Q: 10. 25x2 - 9y2 = 144           11. x2 + y2 = 225           12. x2 + 3y2 = 3

A:

Q: The length of the latus rectum of the ellipse defined by 25x2 +9y2 - 300x – 144 y + 1251 = 0 is 3.0…

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.