Although Type Ia supernovae have been heavily scrutinized due to their use in making cosmological distance estimates, we are still unable to definitively identify the progenitors for the entire population. While answers have been presented for certain specific systems, a complete solution remains elusive. We present observations of two supernova remnants (SNRs) in the Large Magellanic Cloud, SNR 0505-67.9 and SNR 0509-68.7, for which we have identified the center of the remnant and the 99.73% containment central region in which any companion star left over after the supernova must be located. Both remnants have a number of potential ex-companion stars near their centers; all possible single and double degenerate progenitor models remain viable for these two supernovae. Future observations may be able to identify the true ex-companions for both remnants.
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