Find center, foci , vertices, asymptotes and radious of 2x? + 2y² – 28x + 12y + 114 = 0

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 4 – x². What…

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Q: Find the area of the surface formed by revolving the portion in the first quadrant of the graph of…

A: Rearrange the given equation to find y in terms of x and thus f(x). Plot the curve and find the…

Q: Find the center, vertices and foci of the ellipse x? +4 y? - 6 x - 16 y = 39 Select one: O Center =…

A: The standard form of an ellipse whose major axis is parallel to the x-axis is given by  . If then…

Q: 3. Where do the asymptotes intersect for the hyperbola y = ( 2x +3 ) / ( 8x +5 ) O ( 3/8 , 2/5 ) O…

A: Given : Hyperbola y =2x + 38x + 5   To find the asymptotes.

Q: Find the points on the cone z2 = x² + y² that are closest to the point (1,-1,0) %3D

A: Given that, z2=x2+y2 and the point is (1, -1,0). Form the equation of distance as follows.…

Q: Find the points on the cone z = x² + y that are closest to the point (-3,-2,0) %3D

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Q: FINO THE OLUME FORMED BY REVOCVING THE HYPERBOLA xy - from to X=4 about the y- uxis

A: Here the curve is xy=6 and x changes from 2 to 4. we have to find the volume of the given curve

Q: Find the center, vertices and foci of the ellipse x² +4 y² -8 x-8 y= 44 Select one: O Center = (…

A: Equation of the given ellipse is x2+4y2-8x-8y=44. Rewrite the above equation in standard form…

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

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Q: The orthogonal trajectory of y=cex is a parabola of the form y2=ax+b. Find the values of a and b so…

A: See the details solution in below

Q: By differentiating implicitly, find the slope of the hyperboloid x +y? - z = 1 in the r-direction at…

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Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 12 - x. What…

A: Given that the rectangle has its base on x- axis and its upper two vertices on parabola let us take…

Q: 2. x = --(y+ 4)² + 5 y Vertex: Opens: Focus: Directrix:

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Q: The line y = 8.5x+5 intersects the parabola (y-4) = (x-6)2 at points A and B. Point C is on the…

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Q: Find the minimum distance from the point (4,2) to the parabola y2 = 8x.

A: We have to find the minimum distance from the point (4,2) to the parabola y2=8x.

Q: Exer. 1-14: Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. y + 9x² =…

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Q: An ellipse has its major axis on the x-axis, center at ( -3, 0 ), one of the vertices at ( -5, 0 )…

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Q: What point on the parabola y=(6−x)2 is closest to the point (6​,6​)?

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Q: Find an equation of the ellipse with foci at (-4, 3) and (-4, –9) and whose major axis has length…

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Q: Find the standard equation of the hyperbola 1. Asymptotes y=4/3x + 1/3 and y=-4/3x +41/3, a vertex…

A: Solution of the problem as follows

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

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Q: How did he get the value inside the circle Given, 2 = xay2 and x-y+22=2 >2 = 1- - ellipse fox n is…

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Q: -axis. 5. Evaluate dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2, 0, 0),…

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Q: 3. Find an equation of the hyperbola having foci at (4, 3-V 52) and (4, 3 +/52) and asymptotes at y=…

A: Focii: (4, 3+52) & (4, 3-52)Assymptotes : y=3x2-3 , y=-3x2+9Let vertex by represented by (h,k)…

Q: Find an equation of the hyperbola that has fodi at (-15,0) and (15, 0), and asymptotes y=x and y =

A: here we have to find the equation of hyperbola that has foci  at (-15,0) and (15,0) asymptotes…

Q: Find the point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?

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Q: Find the points on the ellipse 3x2 + y2 = 3 that are farthest away from the point (1, 0). What I…

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Q: 13. Find the point on the parabola y* = 2x that is nearest the point (1, 4). %3D

A: As per our guidelines we can solve only one question or three sub-parts. To ask more please…

Q: Find the equation of hyperbola by the given vertices at (0,1) and (0, −1); asymptotes are the lines…

A: Given

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

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Q: Area of the trapezium whose vertices lies on the parabola y = 4x and its diagonals pass through (1,…

A: Here  The vertices lie on the parabola y2=4x and diagonal pass through (1,0) and diagonal length…

Q: The orthogonal trajectory of y= Ce" is a parabola of the form y = ax+b. what is the value of b so…

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Q: What is the largest possible area of a rectangle inscribed in the region bounded by the parabola y =…

A: According to the figure, we have

Q: Hyperbola with vertices (±8, 0), asymptotes y = ±34x

A: At the outset, let me tell you that asymptotes can't be y = ±34x, as stated in the question. It…

Q: 2. Where do the asymptotes intersect for the hyperbola y = -3 / (x + 2 ) -6 %3D O (-18, 6 ) O(-3/2,…

A: A rational function will have a vertical asymptote where the denominator of the rational function is…

Q: Find the points on the cone z = x² + y² that are closest to the point (-5,-2,0)

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Q: A parabola with directrix y = -1 and one endpoint of the latus rectum at (-1,3)

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

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Q: Write the equation for the hyperbola with foci (1,-s), (2.-s) and conjugate axis of length 6. (x-…

A: Please refer the attached image for complete solution.

Q: An isosceles triangle with vertex at (0, -1) is to be inscribed in the ellipse x² + 4y2 = 4. Find…

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Q: What point on the parabola y = 1-x is closest to the point (1,1)? The point on the parabola y = 1-x2…

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Q: What point on the parabola y = 5-x is closest to the point (5,5)? The point on the parabola y = 5- x…

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Q: Find the maximum and minimum values of f(x, y) 3x+y on the ellipse +25 = 1 %3D maximum value:

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Q: 8. Write the equatlon of an ellipse with minor axis endpoints (co-vertices) at (0, 3) and (0, -3)…

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Q: 2. Which equation represents a parabola with vertex (4,4) and directrix y = 2? Oy=2x² - 4x + 4…

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Q: A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the…

A: Introduction :

Q: 20. Parabolas with vertex and focus on the x-axis. llel to the y.

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Q: 1 Find an equation of the hyperbola having foci at (5-/45, 0) and (5+/45, 0) and asymptotes at y = 5…

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Q: Find the vertices and foci of the ellipse. x2 + 3y2 + 2x – 6y + 1 = 0 vertices (x, y) = (smaller…

A: Standard form of ellipse x-h2a2+y-k2b2=1 Foci = h±c,k, where c=a2-b2 Vertices = h±a,k

Q: Determine the coefficients a, b, and c of the parabola y = ax² + bx +c that passes through the point…

A: Solution is here

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.