Ellipse Questions and Answers

Find the equation of the ellipse with the following properties. Express your answer in standard form. Vertices at (-5, -2) and (-5, 12) Minor axis of length 2

Graph the given ellipse. Identify the domain, range, center, vertices, endpoints of the minor axis, and foci in the figure. (x-1)²/4 + (y + 1)²/9 =1 The center of the ellipse is (1,-1). (Type an ordered pair.) The vertices are . (Type ordered pairs. Use a comma to separate answers as needed.)

Consider the following equation of an ellipse. 9x² + 49y² +90x+ 392y + 568 = 0 Step 1 of 4: Rewrite this equation in the standard form of an ellipse. Answer

Consider the following equation of an ellipse. (x+2)^2 /9 + (y-1)^2 /81 =1 Find the center of this ellipse. Answer Enter the coordinates to plot points on the graph. center:

Consider the following equation of an ellipse. (x - 2)²/4+(y + 2)² /16 =1 Step 3 of 3: Find the coordinates of the two foci of this ellipse. Round your answer to two decimal places Enter the coordinates to plot points on the graph.

An arch is in the form of a semi-ellipse, with its major axis as the span. If the span is 80 feet and the height is 30 feet write the standard equation. x²/900+ y²/1600=1 x²/1600+ y²/900=1 x²/6400+ y²/900=1

Find an equation of an ellipse satisfying the given conditions. Foci: (-4, 0) and (4, 0) Length of major axis: 12

Find the equation of the ellipse with the center (6,3), a focus at (3,3), and a vertex at (11,3).

An equation of an ellipse is given. x2/25 + y²/16 = 1 25 16 (a) Find the vertices, foci, and eccentricity of the ellipse.

An elliptical-shaped path surrounds a garden, modeled by (x-22)/225+ (y-26)²/324 =1, where all measurements are in feet. What is the maximum distance between any two persons on the path, and what key feature does this represent? 15 feet; minor axis 18 feet; minor axis 36 feet major axis 225 feet; major axis

An equation of an ellipse is given. (a) Identify the center of the ellipse. (b) Determine the value of a. (c) Determine the value of b. (d) Identify the vertices. (e) Identify the endpoints of the minor axis. (f) Identify the foci. (g) Determine the length of the major axis. (h) Determine the length of the minor axis. (i) Graph the ellipse. Express numbers in exact, simplest form. 9x^2 + 64y^2 = 576

Find the standard form of the equation of the ellipse satisfying the given conditions. Major axis horizontal with length 10; length of minor axis = 4; center: (0, 0). Standard form of the equation:

Consider the standard form of the equation x²/25 + y²/36 = 1 The value of a² is, so the y-intercepts are The graph passes through the ordered pairs which are the vertices. The value of b² is, so the x-intercepts are The graph passes through the ordered pairs The value of a² is, so the y-intercepts are The graph passes through the ordered pairs , which are the vertices. The value of b² is, so the x-intercepts are The graph passes through the ordered pairs

Fill in the blanks so that the resulting statement is true. Consider the standard form of the equation x2 4 + y2 36 = 1 The value of a² is so the y-intercepts are The graph passes through the ordered pairs, which are the vertices. The value of b² is so the x-intercepts are The graph passes through the ordered pairs

Find the standard form of the equation of the ellipse satisfying the following conditions. Major axis vertical with length 12; length of minor axis = 10; center: (7,6) The standard form of the equation is

Consider the equation of the following (x+8)²/4 conic section: + (y + 6)² = 1. Use Desmos and scratch paper to determine the following characteristics of the conic section: Name of Conic Section: Center. Foci: Eccentricity: