Question

Hi, can you help me with this math problem?

The equation of a hyperbola is shown.

`((y-7)^2)/(3)-((x+13)^2)/(12)=1`

Determine the area of the central rectangle.

Answer 1

24

Explanation:

The semi-axis lengths are 'a' and 'b' in the equation ...

(y -k)²/a² -(x -h)²/b² = 1

Area

The area of the central rectangle will be ...

A = LW

The axis lengths are 2a and 2b, so the area is ...

A = (2a)(2b) = 4ab

In terms of the numbers in the given equation, this is ...

A = 4√(a²b²) = 4√(3×12)

A = 4×6 = 24

The area of the central rectangle is 24 square units.