Find the point(s) on the ellipse 4x² + y² = 4 that are farthest 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 an equation of the ellipse that has center (0, 5), a major axis of length 4, and endpoint of…

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Q: Find the equation of the line tangent to the ellipse x + 3y 19 at the point (4,1). (Type an…

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Q: Find the standard form of the equation of an ellipse with vertical major axis with length 16 and…

A: The solution follows as:

Q: Find an equation of the ellipse with minor axis of length 8 and vertices at (-9, 3) and (7, 3).

A: The solution is given in the next step.

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Q: Find an equation of the ellipse that has center (-3, 5), a minor axis of length 2, and a yertex at…

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Q: Show that the line b2xx1 + a2yy1 - a2b2 = 0 is tangent to the ellipse b2x2 + a2y2 - a2b2 = 0 at the…

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Q: image attached

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

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

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

A: Given 4x^2 + y^2 = 4 y^2 = 4 – 4x^2 y = +- (4 – 4x^2)^1/2 Let distance between (x,y) and point…

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Q: Find the standard form of the equation of ellipse satisfying the given conditions as  Major axis…

A: It is given that an ellipse whose major axis is horizontal with length 8, length of minor axis is…

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

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Q: Find the equation of one of the tangents to the ellipse 2x² + 4y² = 48 with slope of mt = 1.

A: The given equation of the ellipse is, 2x2+4y2=48 To find the slope of the tangent to the ellipse, we…

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: What is the equation of the ellipse with the center at (0,0) that passes through the points (2,0),…

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Q: Find the equation of an ellipse centered at the origin with major axis of length 10 lying along the…

A: The standard form of an ellipse centered at origin helps to find the required equation of the…

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Q: Find an equation of the ellipse having a major axis of length 6 and foci at (1, 4) and (1, 0).

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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: Write the standard form equation of the ellipse. Major axis vertical with length 16. Minor axis…

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Q: Find the points on the ellipse 2x +y = 1 where f(x,y) = xy has its extreme values.

A: Introduction: When a multivariable function is to be extremized under some constraints, we use the…

Q: Find equations of both the tangent lines to the ellipse  x2 + 7y2 = 63  that pass through the point…

A: consider (x0 ,y0) be an any point on ellipse

Q: Find an equation of the ellipse that has center (-5, 4), a major axis of length 6, and endpoint of…

A: Length of major axis of an ellipse is 2a

Q: Find an equation of the ellipse having a major axis of length 12 and foci at (0, 5) and (0, 1). =D ?

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Q: Find the equation of the ellipsoid passing through the points (+8, 0, 0), (0,±7,0) and (0,0, ±3) = 1

A: The standard equation of an ellipsoid is x2a2+ y2b2 + z2c2=1where a, b , c are the length of its…

Q: Find an equation of the ellipse having a major axis of length 10 and foci at (-2, 6) and (-2, 0).

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Q: A large racetrack can be modeled by the ellipse x² + y2 1, where x and y are 4 measured in…

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

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Q: find the standard equation of an ellipse centered at the origin whose major axis is horizontal and…

A: We know that standard equation of an ellipse centered at the (h,k) whose major axis is horizontal…

Q: What is the equation of a vertical ellipse with a center at point (8,-4), a major axis that is 12…

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Q: Find an equation of the ellipse that has center (-5, 3), a major axis of length 10, and endpoint of…

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Q: what is the length of the minor axis of the ellipse 5(x+2)2+(y-0.1)2=125?

A: Given5x+22+y−0.12=125

Q: Find the standard form of the equation of an ellipse with the given characteristics. Major axis…

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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…

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Q: An ellipse is centered at the origin and its major axis is on the x-axis. What is the equation of…

A: Explanation of the answer is as follows

Q: Find the distance from the point (3, -4, 2) to the xy-plane

A: Given: 3,-4,2

Q: One successful method to treat kidney stones is by emerging the patient in an elliptical tank and…

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Q: Find an equation of the ellipse that has center (-2, – 1), a minor axis of length 2, and a vertex at…

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Q: find the orthogonal trajectory of family of parabolas represented by the equation…

A: To find orthogonal trajectories of  y2=4ax.

Q: what is the equation of a horizontal ellipse centered at the point (9,4) whose major axis is 22…

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Q: A rectangle is to be inscribed in the ellipse described by x? + = 1. What should the dimensions of…

A: Given,  The equation of the ellipse x2 + y29 = 1  We have to find the dimension of rectangle with…