Find the point on the ellipse x? + 4y? + 2xy = 12 with the greatest x-coordinate. (Use decimal notation and fractions where needed. Give your answer as the coordinates of a point in the form (*,*).) (x, y) =

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A: The equation of parabola parallel to horizontal axis is  x=(y-k)2+h --------------------(1) The line…

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Q: Find the equation of the parabola, y = ax^2 + bx + c, that passes through the points (0,5), (2,-5),…

A: we have to find the equation of the parabola y=ax2+bx+c that passes through the points (0,5), (2,-5)…

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Q: Find the standard equation of the parabola with x intercepts at x = 2 and x -3, and a y-intercept at…

A: Solution is given below

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Q: Find the equation of the parabola given 3 points using quadratic formula. (33,-9) (49,23) (68,3)

A: We have to find the equation of the parabola given 3 points using the quadratic formula. The three…

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

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

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

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Q: Which point or points on the ellipse x? +4y? = 4 are furthest away from the point (0, 1)?

A: The Equation of the given ellipse is, x2+4y2=4 Let the furthest away point on the ellipse, from the…

Q: Find the least and greatest distances from the origin to a point on the ellipse x²+4y²=16.

A: Topic:- geometry

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3.

A: Given :          The equation of directrix of the parabola is x + 1 = 0          The length of the…

Q: Find b and c so that the parabola with equation y = 4x2 - bx - c has a vertex at (2 , 4)?

A: Using the vertex formula we find the x value of the vertex[formula: x value of vertex of Ax^2+Bx+C=0…

Q: Which is the equation of a parabola that has x-intercepts at (2,0) and (-6, 0)?

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Q: Find the equation of the parabola if vertex at (1,-1) the axis of symmetry is parallel to y-axis and…

A: Equation of parabola that have an axis of symmetry parallel to y-axis and the vertex at h,k is…

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

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Q: Find the coordinates of the point on the parabola y = x² which is closest to the point (3, 0).

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Q: A parabola has an equation of y² = 4x. Find the nearest distance from the point (-3, 6) to the %3D…

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Q: Find equations for the osculating circles of the parabola y=0.5x2 at the points (0,0) and (-1,1/2).

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Q: 5. Find the equation of the parabola that has a horizontal axis of symmetry, passing through the…

A: the general equation of a parabola is x=ay2+by+c                            (1) horizontal axis…

Q: Find the point(s) of intersection of the parabola with equation y = x2 - 5x + 4 and the line with…

A: Given equations are,

Q: Find the shortest distance from the point (o, 5) to the ellipse 3y? = x³.

A: We will find the the distance from the given problem.  We know      Distance (D) = sqrt {(x-x1)2…

Q: Find the point (x, y) on the ellipse, 4(x - 1)^2+ y^2 = 1, that is farthest to the origin (0, 0).

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

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

A: Ellipse

Q: Determine the points of intersection of the parabola y=2x^2 +12x +10 and the line y=4x+2

A: I am attaching image so that you understand each and every step.

Q: Find the point on the parabola * +y“ that is closest to the point (0, -3). =

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Q: Find the ratio of the length of minor axis to the length of the major axis of the ellipse 9x2 + 16y2…

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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: Solve for the directrix of the parabola y2 + 8x = 32

A: We have to solve for the directrix of the parabola y2 + 8x = 32.

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

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Q: the center-radius of the equationn 9x²-18 x+ 9+9y? + 12y=12 be obtained by adding both sides of the…

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

A: Given 3x2+y2=3

Q: . Find the equation of the parabola with x-intercepts -7 and 3, and that 2, -11). Express your…

A: Given parabola has two x-intercepts, (-7, 0) and (3, 0). Clearly its either upward or downward…

Q: Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0). (х, у) %3…

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

Q: Find equations for two lines through the origin that are tangent to the ellipse x - 8x + y² + 5 = 0.

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

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Q: Find the area of the largest rectangle that can be inscribed in the ellipse given by: x² + 4y? = 16

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Q: Find the points on the ellipse 3x² + y“ = 3 that are farthest away from the point (1, 0).

A: For the Given Ellipse 3X2+y2=3 ,Points that are  Farthest away from the point (1,0) is calculated as…

Q: Which conic section is represented by the equation 2x2 + 4x - y+9= 0?

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Q: Find the equation of the parabola that is symmetric about y axis with vertex at the origin and…

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Q: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

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: Find the shortest distance of the point (6,3) to the parabola y=x2

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Q: Which is the equation of an ellipse with direcrices at x = =-4 and foci at (2,0) and (-2,0)

A: Center is the midpoint of the foci  midpoint of (2,0) and (-2,0) is : Directrix = -4

Q: Find the equation of the axis of symmetry and the coordinates of the vertex of the parabola given by…

A: Given equation of the parabola is,x = y2 − 2y – 15

Q: Find the point(s) on the ellipse 4x² + y² = 4 that are farthest from the point (1,0).

A: We need to find the points on the ellipse that is farthest from the given point. According to first…