Statement: Every tangent line to the hyperbola intersects the hyperbola only at the point of tangency.

The hyperbola equation is .

Rewrite the equation.

Apply derivative on each side with respect to .

Observe the graph of hyperbola is symmetric about the axis.

Hence if the point is tangent to first part of hyperbola then is the point of tangency for symmetric hyperbola.

Hence the statement is true.

The statement is true.