2. Put the equation in standard form then sketch a graph indicating the foci and end points: 9x2 + 36x + 4y² – 24y + 36 = 0

Q: Graph the ellipse 9(x - 1)2 + 4(y + 3)2 = 36 and give the location of its foci.

A:

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: Use the graphs of y 2 and y = 4x 10 5. shown below, to complete the following %3D %3D sentence. The…

A: Given two graphs are y=2 and y=-4x-105.

Q: the full question is clearly indicate the center , endpoints of the major and minor axes and the…

A:

Q: A nerd guitarist attempted to measure the auxiliary rectangle from the dips of his preloved electric…

A: The standard form of a hyperbola with the traverse axis on the x axis is x-h2a2-y-k2b2=1.  Here h,k…

Q: Determine the graph of the equation a² + y² + 2² - 6x + 2y - 4z + 19 = 0. O Sphere O Point O Empty…

A: Given :x2+y2+z2-6x+2y-4z+19=0

Q: Rewrite the equation 4x2 + 3y2 – 16x – 12y + 16 = 0 to standard form and identify the coordinates of…

A: The given equation is 4x2+3y2-16x-12y+16=0. We need to first rewrite it to standard form. The have…

Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (0, ±5), length of…

A: Given that hyperbola satisfies the following conditions: Foci=0,±5  and length of transverse axis is…

Q: 2. Sketch and identify the graph of the equation a + y? – 2y –- 3 = 0 in 3D.

A: x2+y2-2y-3=0x2+y2-2y+1-4=0x2+(y-1)2=4The equation represents circle in 2D,but a cylinder of radius 2…

Q: In a parabola, the directrix has equation x = 1 and the vertex is at (3, 1). What are the…

A:

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: 2. Sketch and identify the graph of the equation a+y? - 2y-3 0 in 3D.

A:

Q: 3. Write an equation for the parabola with focus (1, 3) and vertex (0, 3). a. y = 4(x – 3)² b. y =…

A: Given:      focus =1,3      vertex =0,3  The focus and vertex are horizontally aligned, so the…

Q: 5. Identify the focus of the parabola given by y = 8x². O (0,) O (-8,0) O (0,0) O (8)

A:

Q: 20) Rewrite the equation in standard form, indicate the features and sketch the graph with accuracy.…

A:

Q: Rewrite the equation from vertex form to standard form. Vertex Form: y = - 1(r – 3) – 4 Standard…

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: b) Express the equation of a circle 3x2 +3y2 + 42x = 12y - 111 in standard form. Then, identify and…

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Q: Graph: x2 + 4y2 + 10x + 24y + 45 = 0. Where are the foci located?

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Q: 1) Graph 3x* +8у? %3D72 Also graph the foci.

A:

Q: (æ – 6)?, (y – 4)? Given the ellipse 4 + Find the center point: List the four vertices:

A: We need to find the center point and the vertices.

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: Graph the parabola with a focus of ( – 2, 1), a directrix of y = 7, and goes through the point (4,…

A: We have to find the equation of parabola.

Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (+10, 0), length of…

A: The foci of the hyperbola are ±10,0 and the length of the transverse axis is 16. The objective of…

Q: Which graph corresponds to an ellipse with foci located at ((2+2√5), 6) and ((2−2√5), 6) and the…

A:

Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (±5, 0), length of…

A: We will find the equation of hyperbola.

Q: Find the coordinates of the points of intersection of the parabola y = x2 and y = x+3.

A:

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

A: Sketch the Equation of ellipse

Q: What are the foci of the ellipse given by (x-3 )^2/25 + ( y−1)^2/9 = 1 ?

A: By using standard form and ellipse, we calculate the foci of an ellipse.

Q: Express the general form to its standard form and locate the center, vertices, covertices and foci…

A: equation 4x2 - y2 - 32x - 4y + 24 = 0

Q: I llustiate and Sketch the equation of parabola ?f vertex

A: General equation of parabola is of form y2=4ax or x2=4ay

Q: Find the verticles, foci and graph a) y=2x2-8x+3

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

Q: 14. y = 2x- 12x + 10 Axis of Symmetry: Vertex: Sketch:

A: Given

Q: 13–22, write the standard form of the equation and the general form of the equation of each circle…

A: Standard form: (x-h)2+(y-k)2=r2 Given (h, k)= (0,0) and r = 2.  Answer: Standard form:…

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: Suppose the graphs of y = 5x? – 4x + 9 and y = x – 4x² – 2x + d intersect at a = 8. Find all…

A:

Q: Write the equation of the hyperbola of foci F1(2, −1), F2(2, 4) and focal radius difference equal to…

A: The equation of hyperbola can be obtained from the foci and the vertices or other parameters. If the…

Q: Find the vertex, focus, foci and directrix of the parabola (x-6)^2+8(y+7)=0 and sketch its graph

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Q: Draw the graphs of the equations x – y+1=0 and 3x+2y – 12=0. Determine the coordinates of the…

A: Sketch the given equations:

Q: Find the vertices and foci of the ellipse: 6. (x-1) (y+3)? = 1. Round to nearest tenth if…

A: Given- x-129+y+3236=1 To Find- The vertices and focii of the ellipse.

Q: 2. PARABOLA VERTEX = (2, FOCUS = (1,

A: Given vertex=2,1 and focus=1,1 We have to find the equation of the parabola. We can see that the…

Q: Suppose the graphs of y = 4x? 9x – 1 and y = x³ + bæ² + 17x + 111 intersect at x 2. %3D Find all…

A: Solution: The objective is to find the intersection points

Q: 1. Change the given equation from general form to standard form, identify the vertex, focus,…

A: The standard form of the parabola is (x-h)2 = 4p(y-k), convert the given equation into standard…

Q: Which equation represents the ellipse with vertices located at (3, -3) and (3, -13) and foci at (3,…

A: Answer

Q: Find the standard equation of the parabola which satisfies the given conditions. Vertex (−8,3),…

A: To find the standard equation of parabola

Q: 1. Express the following equation in vertex form: y coordinates of the vertex point. 2 = 3x² 12x +…

A:

Q: The focus of a parabola is (-3,5) and the directrix is y = -1. Which equation represents a parabola…

A: Given: the focus of a parabola -3,5 and the directrix is y=-1 Formula: Distance between point x,y on…

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.