Find the area of the greatest rectangle that can be inscribed in the ellipse \frac{x\power{2}|a\power{2}}+\frac{y\power{2}|b\power{2}} = 1. The auxiliary circle of a family ofellipses passes through the origin and makes intercepts f 8 units and 6 units on the x-and y-axes, respectively. If the eccentricity of all such ellipses is 1/2, then find the locus of

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A: Given problem is : Find the equation of the circle Busan bent X=y^2-y at point (0,1) .

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A: GivenP(6.0)y2=8x To find nearest distance

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A: Let P be (acosθ, bsinθ), then the equation of tnagent at P is         xacosθ+ybsinθ=1Slope of…

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A: We given that a ellipse  x225+y216=1 with midpoint (1/2 , 2/5 ).   Claim : we have to find the…

Q: What is the most time-consuming part in using a graphing utility to graph a general second-degree…

A: To discuss about graphing utility.

Q: Define hyperbola with reference to algebra.

A: Define the hyperbola

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A: Firstly the trace of a surface which is actually a cross section or the curves of intersection of a…

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A:

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Q: given the following equation: 36y^2-4x^2=144.  a) determine if the function is an ellipses or a…

A: This question can be solved using the concept of conic section.

Q: The length of the latus rectum for the ellipse x^2/64 + y^2/16 = 1 is equal to

A: Explanation of the answer is as follows

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A: Length of the major axis is 477,736 Length of the minor axis is 477,078 We need to calculate the…

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A: According to the given question, the initial account balance is $50,000. The rate of interest is 5%…

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Q: a parabola which opens downward with endpoints of latus rectum in (-3,3) and (3,3) what is the…

A: Given are the end points of latus rectum of a parabola which opens downwards .The objective is to…

Q: 4. Find the equation of the ellipse assuming the form + = 1 if distance between foci 4, between…

A: Use simple standard equation

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A:

Q: Determine the equations of the tangents drawn from the point P(5,-3) to the ellipse x² + 4y² + 2x -…

A:

Q: Find the locus of the midpoints of a focal chord of the ellipse…

A: The equation of the given ellipse is                                   x2a2+y2b2=1.

Q: A water tower has a right circular cylindrical tank oriented vertically with radius 3 m and height 6…

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Q: compute the acute angle formed by the asymptotes of the hyperbola x^2-3y^2-8x=14

A: Explanation of the answer is as follows