Question

The symmetry of a hyperbola with a center at (h, k) only occurs at y = k.

True or False

Answer 1

The given statement is a False statement.

Explanation:

We know that the center of a hyperbola is the mid-point of the transverse axis of the hyperbola.

If the curves of hyperbola opens up and down such that the center is (h,k) then the symmetry of hyperbola is:

y=k

and if the curve opens to the right and to the left and the center is at (h,k) then the symmetry of hyperbola is:

x=h

Hence, the statement:

The symmetry of a hyperbola with a center at (h, k) only occurs at y = k.

is FALSE.