If the focal distance of an end of theminor axis of an ellipse (referred to its axes as the axes ofx and y, respectively) is k and the distance between its foci is 2h, then find its equation.

Q: X y² Find the eccentricity of an ellipse- + a² b² = 1 whose latus rectum

A: Let a>b. Then the latus rectum ofthe ellipse is 2b2/a and the semi-major axis is a.       Given…

Q: Find the equation, foci, and directrix of the standard ellipse with eccentricity e = 0.6 and focal…

A: The ellipse is a horizontal ellipse as focal vertices lie on the x - axis. Let the standard equation…

Q: Consider the ellipse whose vertices are ( ±4,0) and the y- intercepts are ±1. Find the implicit…

A: Step 1:To find the implicit equation of the ellipse, we need to remember that the standard form…

Q: 4. Determine the equation of an ellipse having foci (0, ±9) and major axis length 22.

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Q: 6. Find the Equation of the Ellipse whose Vertices and Foci are at (0, ±17) and (0, ±9)…

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Q: Find the equation on the ellipse that has its center at the origin and satisfies the conditions:…

A: We have to find the equation on the ellipse that has its center at the origin and satisfies the…

Q: The graph of x+6xy+ 25y = 16 is an ellipse. Find the coordinates of the points where the ellipse has…

A: see below the answer

Q: Write the equation of the ellipse centered at the origin with a vertex at (-6, 0) and a co-vertex at…

A: A detailed solution is given below.

Q: find the important parts (vertex, focus, directrix, endpoints of latus rectum and focal point…

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Q: One focus of a hyperbola lies at the point (0, -7) and the cor-responding directrix is the line y =…

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Q: Find the equation of the ellipse in standard form centered with foci located at the (4, -5) and (-8,…

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Q: An ellipse can be defined parametrically by (your birth month cos t + 1, your birth date sin t – 2).…

A: The standard equation of an ellipse centered at (h,k) is given by: The parametric form of such an…

Q: 1. Write the standard equation for the ellipse whose minor axis is the line segment from (0, -2) to…

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Q: Find the DE of an ellipse with the equation: +2²=1

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Q: What is the standard form equation of the ellipse that has vertices (0, ±12) and foci (0, ±2)?

A: We know that the standard equation of the ellipse is (x-h)^2/b^2+(y-k)^2/a^2=1

Q: Find the axes of this tilted ellipse 5x2 + 8xy + 5y? = 1, and sketch the graph of both ellipses.

A: Consider the general equation for the ellipse and compare the given equation to the general equation…

Q: Eliminate the parameter, An ellipse: x = h + a cos t, y = k + b sin t. Write the resulting equation…

A: Let's consider the given equations for the ellipse:…

Q: 6. a. Give the equation of the conic shown below. Equation: b. Find the two focal points and plot…

A: The given figure is an ellipse. Consider the general ellipse:

Q: Identify this conic, list the necessary parts and then graph it: 2x2 +2y2 +8x=7

A: Given the equation of conic

Q: Find the equation of the ellipse with the given properties: Vertices at (+25,0) and (0, 164)

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Q: Find the equation of the ellipse whosefocus is S(-1, 1), the corresponding directrix is          x…

A: Let P(x,y) be any point on the ellipse and PMbe perpendicular to the directrix.…