Question

Find the equation to the hyperbola, referred to its axes as axes of coordinates.

(a) whose transverse and conjugate axes are respectively 3 and 4, whose foci is 13

(b) whose conjugate axis is 5 and the distance between whose foci is 13

(c) whose conjugate axis is 7 and which passes through the point (3,-2)

• A. (a) whose transverse and conjugate axes are respectively 3 and 4, whose foci is 13
• B. (b) whose conjugate axis is 5 and the distance between whose foci is 13
• C. (c) whose conjugate axis is 7 and which passes through the point (3,-2)

Answer 1

Answer: (B), (C)

(b) and (c)

Answer 2

Part (a) is inconsistent as $c^2 \neq a^2 + b^2$. For part (b), $a^2$ is calculated using $c^2=a^2+b^2$, yielding two possible equations based on transverse axis orientation. For part (c), $a^2$ is found by substituting the given point into the standard equations for both orientations, yielding two distinct equations.