  We study central simple algebras with involution of the first kind that
become hyperbolic over the function field of the conic associated to a given
quaternion algebra $Q$. We classify these algebras in degree~4 and give an
example of such a division algebra with orthogonal involution of degree~8 that
does not contain $Q$ with its canonical involution, even though it contains $Q$
and is totally decomposable into a tensor product of quaternion algebras with
involution.
