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

Q: Find the length of the chord of the ellipse \frac{x\power{2}|25}+\frac{y\power{2}|16}=1  whose…

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: Sketch the Ellipse with the equation x^2/81 + y^2/16 = 1

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Q: Define hyperbola with reference to algebra.

A: Define the hyperbola

Q: Determine the vertical traces of elliptic and parabolic cylinders in standard form.

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

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT PLEASE Determine the equations of the tangents to the ellipse…

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Q: What is the family of curves for all parabolas with axes parallel to the y-axis.

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Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

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Q: There are four questions about this problem in the test shown in random order. Out of 1000 customers…

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Q: X y² Find the eccentricity of an ellipse- half of its maior axis + I a² b² = 1 whose latus rectum is

A: Given: Here is the given ellipse, x2a2+y2b2=1 Latus rectum=12× major axis. To find: The…

Q: The length of the major axis of an ellipse with foci at (-1, 2) and (3, 2) that passes through the…

A: Here we use basic defnition of major axis

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

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

Q: state the center, vertices, equations of asymptotes, and the foci of the following equation x^2/9 -…

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

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Q: Let 4x^2+3y^2+8x-6y=5 find the center and foci. Graph

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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