Eccentricity-directrix approach Find an equation of the following curves, assuming the center is at the origin. Sketch a graph labeling the vertices, foci, asymptotes (if they exist), and directrices.Use a graphing utility to check your work. A hyperbola with vertices (±1, 0) and eccentricity 3

Q: a) Find the standard equation of a circle, which the diameter has endpoints (1, 4) and (5, 4).…

A: We have to find the standard equation of a circle, which the diameter has endpoints (1, 4) and (5,…

Q: Eccentricity-directrix approach Find an equation of the following curve, assuming the center is at…

A:

Q: 1. Consider the parabola with focus point (1, 1) and directrix the horizontal line y = -3. a) What…

A:

Q: A lamp with a parabolic reflector is shown in the figure. The bulb is placed at the focus and the…

A:

Q: Find an equation for the hyperbola that satisfies the given conditions. Asymptotes: y = x, hyperbola…

A: To find an equation for the hyperbola that satisfies the given conditions.Asymptotes: y=±x,…

Q: A lamp with a parabolic reflector is shown in the figure. The bulb is placed at the focus and the…

A: (a) The parabola is right oriented, so the equation of the parabola is of the form y2=4px where p is…

Q: The graph above shows a parabola. 1. The focus of the parabola is located at ( 2. The directrix of…

A: We know that parabola is a set of points in a plane which are equidistance from a given point and a…

Q: Eccentricity-directrix approach Find an equation of the following curves, assuming the center is at…

A: Consider the general ellipse:

Q: Find an equation of the parabola that has a focus at (2, 17) and a vertex at (2, 9) y = Find an…

A: Follow the procedure given below.

Q: Parabolas with axis parallel with the y-axis and with distance from vertex to focus fixed as a. Ans.…

A: The given problem is to find the differential equation for the given parabolas with axis parallel…

Q: Put the equation in standard form and find the hyperbola’s asymptotes. Then sketch the hyperbola.…

A: A hyperbola is the locus of a point in a plane which moves in the plane in such a way that the ratio…

Q: Derive the equation x² = 4py in Figure 10.4.6.

A: Parabola - A parabola is a curve, in which any point on the parabola has equal distance from a fixed…

Q: Find an equation for the hyperbola described.Graph the equation

A: Given: Foci: 0,-2 and 0,2Asymptote the line: y=-x To Find: Equation of the Hyperbola.

Q: An equation of a parabola is given. (a) Find the focus, directrix, and focal diameter of the…

A: Given, The equation of the parabola y=18x2 We have to find  focus, directrix and focal diameter of…

Q: parabola with vertex on the x axis parallel to the y axis and with distance from the focus to vertex…

A:

Q: The foci of the hyperbola are (0, -17) and (0, 23), and the asymptotes are y = x + 3 and y = - x +…

A:

Q: Find an equation of the parabola that has a focus at (6, 11) and a vertex at (6, 8) y = Find an…

A: Equation of parabola with vertex (h,k) x-h2=4ay-k Focus : (h, k+p ) equation of directrix y = k-a…

Q: Given the focus and directrix of the graph of a parabola (image shown below) identify the following:…

A:

Q: Find an equation for the hyperbola described.Graph the equation

A: Consider the given: General equation of hyperbola:y2a2−x2b2=1,which has two oblique asymptotes of…

Q: Find an equation for the hyperbola described.Graph the equation

A: Given: Foci -4,0 and 4,0asymptote the line y=-x

Q: Find an equation of a parabola satisfying the given information. Focus (9, 1), directrix x= - 10 An…

A:

Q: Find the equation of the parabola described. Directrix the line y=3; vertex at (0,0)

A:

Q: Hyperbola, eccentricity 3, directrix r =- 6 csc θ

A:

Q: Find an equation of the parabola that has a focus at (9, 6) and a vertex at (9, 5): y = Find an…

A: Use general equation of parabola

Q: Question 18

A:

Q: 4. Find the equation of the parabola with focus at (0, 6) and the directrix defined by the equation…

A: 5

Q: Find the eccentricity of the hyperbola. Then find and graph the hyperbola's foci and directrices. x²…

A: use the formula for eccentricity of hyperbola

Q: 1. center a. the middle of the hyperbola 2. branches b. the line segments connecting the foci that…

A: A hyperbola will have a centre , two focii ,transverse axis and two asymptotes.

Q: A hyperbola has vertices at (-3, 0) and (3,0). Its foci are located at V34, 0 and (-V34,0). You must…

A:

Q: Please provide me a complete and clean solution.  Let P be the parabola with focus at F(−1, −2) and…

A: let   P'(x, y)  be any point on the parabola  focus of parabola  F -1 , -2 and   M be the point on…

Q: An equation of a parabola is given. y = -x2 (a) Find the focus, directrix, and focal diameter of the…

A:

Q: Find the equation of the parabola with the given information. Find the two points that define the…

A:

Q: A parabola can be drawn given a focus of (7, –3) and a directrix of y = 9. Write the equation of the…

A: on solving this we get the

Q: The hyperbola with equation - E = 1 has asymptotes y =+x and foci (±13,0). Find the values of a and…

A: For the detailed solution of the problem follow the next steps.

Q: Eccentricity-directrix approach Find an equation of the following curves, assuming the center is at…

A:

Q: Find an equation of the parabola whose graph is shown. y Focus Need Help? |Talk to a Tutor aster…

A:

Q: Find an equation for the hyperbola that satisfies the given conditions. Asymptotes: y = +x,…

A: given asymptotes y =±x  the center of the given hyperbola is (0,0) the asymptotes will be given by…

Q: a parabola with vertical axis with focus at (2,1) and whose latus rectum has length of 4, find the…

A: The standard form of the parabola with the vertical axis is: (x-h)2=4a(y-k)                ....(1)…

Q: The x- and y-coordinates of the focus of a parabola are (1,3) and the directrix is y = -5. A second…

A: Given Foucs of parabola=1,3and directrixy=-5

Q: An equation of a parabola is given. 1,2 y = (a) Find the focus, directrix, and focal diameter of the…

A: I am going to solve the given problem by comparing it standard form of parabola to get the required…

Q: The graph of a hyperbola is given below. The equations for the two asymptotes are y =x - y = -x+ Use…

A: The equations of the asymptotes are y=23x-23 and y=-23x+143. Asymptotes of the hyperbola passes…

Q: Find an equation of a parabola satisfying the given information. Focus (8, 5), directrix x = - 9 An…

A:

Q: Conic sectionsa. Determine whether the following equations describe a parabola, an ellipse, or a…

A: Given, x2-y22=1

Q: Question: Find an equation of the parabola that has a focus at (2, 11) and a vertex at (2, 8): y =…

A:

Q: y For the hyperbola given by the equation: =1; find all of the requested information and then 25 9.…

A: Solution

Q: Find the equation of the parabola described. Find the two points that define the latus rectum, and…

A: Given- Directrix line y=-12and the vertex at 0,0. To Find- The equation of the parabola and find the…

Q: Two radio transmitters are 1000 mi apart at points A and Balong a coastline. Using LORAN on the…

A:

Q: Eccentricity-directrix approach Find an equation of the following curves, assuming the center is at…

A: An ellipse with vertices (0, ±9) and eccentricity 1/4.  Find an equation of the following curves,…

Q: A parabola has the equation 6x + y = 0. (a) Find the focus and directrix of the parabola, and sketch…

A: