Hyperbola Questions and Answers

A table lamp emits light in the shape of a hyperbola If the hyperbola is modeled by the equation 25x 144y 2 3 600 0 which of the following equations represents the boundaries of the light Oy 5 12 5 x and y 12 X Oy 12x and y 12x 5 5 5 Oy x and y x X 13 13

Your mission is to track incoming meteors to predict whether or not they will strike Earth Since Earth has a circular cross section you decide to set up a coordinate system with its origin at Earth s center The equation of Earth s surface is x y 40 68 where x and y are 2 2 distances in thousands of kilometers You observe a meteor moving along a path from left to 240 60 where right whose equation is y 14 x 60 289 y 5 5 What conic section does the path of the meteor travel The meteor s path is a n What is the center of the conic section that describes the path of the meteor Determine if the meteor will strike the earth and if it does strike the earth at what point If the meteor doesn t strike the earth then enter NAN for

Find the standard form of the equation of the hyperbola satisfying the given conditions. x-intercepts ±6, foci at (-10,0) and (10,0)

Use vertices and asymptotes to graph the hyperbola. State the coordinates of the vertices. Find the equations of the asymptotes. 1) (x^2/4)-(y^2/16)=1

Given an hyperbola which passes through point P has vertices V, and V₂, and has foci F, and F₂, which of the following statements is a fact about hyperbolas? Choose the correct statement below. A. If 2a is the length of the conjugate axis, then |d (P,V₁)-d(P,V₂)|= 2a. B. If 2a is the length of the transverse axis, then d (P,F₁)-d(P,F₂)|=2a. C. If 2a is the length of the transverse axis, then |d (P,V₁)-d(P,V₂)|=2a. D. If 2a is the length of the conjugate axis, then |d (P,F₁) -d (P,F₂)|=20.

Find the standard form of the equation of the hyperbola satisfying the given conditions. x-intercepts (±4,0); foci at (-5,0) and (5,0) The equation in standard form of the hyperbola is

Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an answer does not exist, enter DNE.) (x^2)/9 - (y)^2/25 =1

Write an equation for the hyperbola with center at (5, – 4), focus at (8, – 4), and vertex at (7, - 4). An equation for the hyperbola is ____ .

The cross-section of a nuclear power plants cooling tower is in the shape of a hyperbola. Suppose the tower has a base diameter of 264 meters and the diameter at its narrowest point, 56 meters above the ground, is 88 meters. If the diameter at the top of the tower is 176 meters, how tall is the tower?

Find an equation for the hyperbola described. Graph the equation. Foci at (2,3) and (10,3); vertex at (7,3) Write an equation for the hyperbola. (Type exact answers for each term, using fractions as needed.)

Fill in the blank so that the resulting statement is true. The equations for the asymptotes of x² 64 - y² 81 = 1 are

The cross-section of a nuclear power plant's cooling tower is in the shape of a hyperbola. Suppose the tower has a base diameter of 210 meters and the diameter at its narrowest point, 48 meters above the ground, is 70 meters. If the diameter at the top of the tower is 140 meters, how tall is the tower?

Find an equation for the hyperbola described. Graph the equation by hand. Center at (0,0); focus at (0,8); vertex at (0,4) An equation of the hyperbola is

Determine the direction of opening or openings for the hyperbola (x-3)²/9 - (y+4)²/4 = 1 a. Left b. Up c. Left and right d. Up and down

A hyperbola has vertices (1,2) and (3,2). Which of the following equations could represent this hyperbola? Select all that apply.

7. Given the following information, write the standard form equation of each hyperbola and determine the equations for the asymptote lines of the hyperbola. a. Vertices: (-5, 5), (-5, 3): Foci: (-5, 6), (-5, 4) b. Vertices: (-10, 1), (-10, 17); Perimeter of Central Rectangle = 76