Determine the relation of the ellipse x + 4y = 32 and the line 2x +y-1 0.

Q: 4. Determine whether the graph of the equation is a hyperbola or a pair of two intersecting lines.…

A: (a) Given,             25x2-16y2-250x+128y-31=0

Q: Find an equation for the ellipse whose graph is shown. y F(0, 4) 4

A: find explanation below

Q: Which graph represents the ellipse given by x^2/20+y^2/28=1?

A: We need to identify the graph of ellipse x^2/20+y^2/28=1

Q: Write the equation of a parabola whose directrix is y = 0.25 and has a focus at (-1, - 2.25).

A:

Q: In which direction does the parabola x = -y 2 + 3 open?

A: x=-y2+3 There are two patterns for a parabola, as it can be either vertical (opens up or down) or…

Q: Which graph represents the ellipse represented by the equation (x−4)^2/4 + (y−1)^2/25=1?

A: Given (x-4)24+(y-1)225=1

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: Write the equation of the ellipse 9x2 + 25y² – 54x – 50y – 119 = 0 in standard form (x – h)² (y –…

A:

Q: Find the equation of ellipse whose vertices are(-1,-4) (-1,8) and focus is at(-1,6).

A:

Q: 6. What is the equation for the slope of the ellipse+-1 at 1 at (x₁, ₁)? A. B. C. D. E. y' = -21 y'=…

A:

Q: Find an eguation of the ellipse with Focilo,a) and (0,-2) and verticesco,3) and C6,-3).

A:

Q: Determine the relation of the ellipse x + 4y° = 32 and the line 2x +y-1 0.

A: To Determine: the relation between the ellipse x2+4y2=32 and the line 2x+y-1=0 Given: we have two…

Q: Find the equations of two lines through the origin that are tangent to the ellipse 2x - 6x+y +4 = 0

A: Consider the given equation:2x2−6x+y2+4=0Let a line y=mx+c is a tangent to the ellipse.Tangent…

Q: Describe the graph of the equation X² −y² −4x + 8y−21 = 0

A: x2-y2-4x+8y-21=0

Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2)

A:

Q: Sketch the parabola and line on the same graph. y = x + 4 and y = 2x + 2 %D

A: Consider the given parabola y=x2+4 and the line y=2x+2. Use online graphing calculator and sketch…

Q: Find the intersection points of the pair of ellipses. (100x² + 25y² = 100 y? x2 + (х, у) %3 (smaller…

A: In this question we will use basic of algebra i.e solutions of two equation which are the point of…

Q: Graph the ellipse. (x + 2)² (y + 2)² =1 + 25 16

A: The ellipse can be graphed as below.

Q: Which graph represents the ellipse given by x^2/4+y^2/1=1?

A: Given equation of ellipse is x24+y21=1. We know that the standard equation of ellipse is given as:…

Q: Find the points on the ellipse x^2 + 9y^2 = 9 and the line x + y = 10 that are closest and farthest…

A: Distance between the two points: - The length of the line segment connecting two places is called…

Q: Find the equation of the parabola whose focus is (-2,-15/4 ) and whose directrix is y = -17/4.

A: Given focus of parabola is    -2, -154 and directrix is    y=-174

Q: The ellipse with x-intercepts at (7, 0) and (-7, 0), y-intercepts at (0, 5) and (0, -5), and center…

A: Rhis problem is related to conic section and we solve this problem using standard form of the…

Q: Find the points of intersection between the line 4y - 3x + 12 = 0 and the ellipse 9x 2 + 16y 2 =…

A: The line 4y-3x+12=0 And the Ellipse 9x2+16y2=144 We need to find the intersection point of the line…

Q: Which of the following is the domain and range of the ellipse with equation x² + 4y²2 - 2x + 16y-…

A:

Q: Rewrite the given equation of a quadratic surface and identify the graph. 12y2 – 3z2 = 16x -

A: Rewrite the equation as z2 in terms of x and y.

Q: Find the evolute of the ellipse x2 / a2+y2 / b2=1.

A: The given ellipse has the equation:

Q: Graph the ellipse. 10x² + 2y? = 5 -2 4 -4 2 4 y y 2

A:

Q: Which graph represents the ellipse given by x^2/20+y^2/8=1?

A: Sketch the Equation of ellipse

Q: find the standard equation of the ellipse convertices (-11,4) and (-3,4), a focus at (-7,11)

A: Given:- Co-vertices  (-11,4) and (-3,4), a focus at (-7,11) To find:- Standard equation of ellipse

Q: 2) Graph the ellipse (x−1)² _(y+5)² 4 9

A: Solution: here we are using the graphing tool to plot an ellipse.

Q: Sketch the parabola and line on the same graph. y = x2 + 4 and y = 2x + 2

A: Given, y=x2+4   y=2x+2  The graph of given functions can be plotted as shown in the figure below.

Q: (-3x) dxtxdy C is part of the ellipse 5x2+6y=30 fromC0,-V5) to cra,O). X,

A: Line integral Given ellipse is  From .

Q: Classify the graph equation 2x^2-4y^2+4x+8y-3-0

A: Given : The equation 2x2-4y2+4x+8y-3=0.   To classify : The graph equation 2x2-4y2+4x+8y-3=0.

Q: Graph the ellipse. (x – 5)² + (y + 2)² 52 42 y y 10- 10| - 10 -5 10 - 10 -5 10 -5 - 10F - 10 y y -10…

A: As per guidelines, I can answer only three subparts of a question.

Q: Write the equation of a parabola whose directrix is y = 7.5 and has a focus at ( – 4, – 4.5). -

A: The equation of parabola whose directrix is y=-7.5 and has a focus at (-4,-4.5).

Q: Assume the equation of a parabola and a line are given by y = x +2 x and y =3 x +6, respectively.…

A:

Q: Identify the graph of the ellipse given by *+7*,-) 49 25 16- 14 12 10-

A: The answer is option 3

Q: A- Sketch the graph of ellipse: - (x-1)2 + y? = 0. 4

A: A) we use the standard forms (x-h)2a2+(y-k)2b2=1 The center of the ellipse is (h,k). Now, to compare…

Q: for the ellipse 4x^(2)+y^(2)+24x-2y+21=0, find the vertices

A:

Q: Find an equation of the parabola whose graph is shown. y X (4, –2)

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

Q: Find the slope of the ellipse x^2 + 4y^2-10x- 16y +5=0 at the point where y=2+ 8 0.5 and x-7* O…

A: Given equation of the ellipse is as following: x2+4y2-10x-16y+5=0. We know that the slope of an…

Q: Graph the ellipse (x - 2)2/9 + (y - 1)2/4 = 1 and give the location of its foci.

A: Given equation of ellipse is (x-2)29+y-124=1

Q: What is the distance between the vertices of the ellipse: 64x^2 + 25y^2 _ 16x - 16y-648= = 0? C.…

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.