A hyperbola has foci (1, 3) and (1, -3), and a vertex (1, 1).

Question

1Find the standard form of equation of a hyperbola.

2For any point on the hyperbola, what is the absolute value of the difference of its distances

from the foci?

3A vertex is at,

4What are the asymptotes?

5Determine the length of the conjugate axis.

Graph it

Answer 1

2c = 6; c = 3; Center at (1, 0); a = 1; b² = 9 - 1 = 8; a = 2√2;

1. y²/1 - (x - 1)²/8 = 1
2. Id₁ - d₂I = 2