Ask Question
2 December, 15:24

a hyperbola has a center at the origin, a vertex at (9,0) and a focus at (41,0). What is the equation of the hyperbola

+3
Answers (1)
  1. 2 December, 16:22
    0
    the equation of the hyperbola is; (x²/81) - (y²/1600) = 1

    Step-by-step explanation:

    We are given that the hyperbola has;

    Centre; 0,0

    Vertex; 9,0

    Focus; 41,0

    Thus, the vertex and focus are on the x-axis. Thus, the equation for the hyperbola will have the form;

    (x²/a²) - (y²/b²) = 1

    Since The vertex is (9,0), so

    a = 9 and a² = 9² = 81

    Also, Since The focus is (41,0), so

    c = 41 and c² = 41² = 1681

    Solving for b², we have;

    b² = c² - a²

    b² = 1681 - 81

    b² = 1600

    b = √1600

    b = 40

    Thus, equation of hyperbola is;

    (x²/9²) - (y²/40²) = 1

    Which gives;

    (x²/81) - (y²/1600) = 1
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “a hyperbola has a center at the origin, a vertex at (9,0) and a focus at (41,0). What is the equation of the hyperbola ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers