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

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