Q1. What is the equation of the hyperbola whose latus rectum has length 8 and whose eccentricity is 3/√5?
A x^2/25 - y^2/20 = 1 Correct
B x^2/20 - y^2/25 = 1
C x^2/16 - y^2/25 = 1
D x^2/25 - y^2/16 = 1
Explanation
For a standard hyperbola x^2/a^2 - y^2/b^2 = 1, eccentricity satisfies e^2 = 1 + b^2/a^2. With e = 3/√5, e^2 = 9/5, so b^2/a^2 = 4/5. The latus rectum length is 2b^2/a = 8, hence b^2 = 4a. Combining these gives a = 5, so a^2 = 25 and b^2 = 20. Therefore the equation is x^2/25 - y^2/20 = 1. The other equations have the wrong values or interchange the denominators.