Hyperbola Questions and Answers

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

Consider the equations below and complete the following: Before completing any calculations, consider the equation and write down an educated guess as to which type of conic section is represented. Explain briefly how you made your prediction. Complete the square to rearrange each equation into standard form and identify the conic section. Compare the equation in standard form to the original version. Look closely at the coefficients of each term (specifically which terms are positive or negative). Is there anything you notice that is similar between the two equations? How can this help you to identify conic sections that are not in standard form? a. x² + y² + 6x - 4y - 15 = 0 b. 49x² + 196x + 4y² - 40y + 100 = 0 c. x² - y² - 2x - 8=0

A telescope contains both a parabolic mirror and a hyperbolic mirror. They share focus F₁, which is 42 feet above the vertex of the parabola. The hyperbola's second focus F2 is 6 ft above the parabola's vertex. The vertex of the hyperbolic mirror is 3 ft below F₁. Find the equation of the hyperbola if the center is at the origin of a coordinate system and the foci are on the y-axis. Complete the equation.