A member of the missing Australian family-of-four, the Langfords, has reportedly been found alive.

Jesse Langford, 19, was presumed dead following the eruption. His sibling and parents are still missing.

Father Anthony, 51, mother Kristine, age unknown, and sister Winona, 17, all remain unaccounted for.

The family were initially listed as missing on the New Zealand Red Cross' Registrar.

Jesse and his family were touring the volcano on Monday as part of a cruise holiday.

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A Sydney family is missing, feared dead, following the New Zealand volcano. Video / 7 News

Anthony's brother Rodney told 7NEWS on Tuesday he was maintaining hope the family-of-four had survived.

"We don't know anything at all," Langford said.

"But I'm hoping that somebody knows anything, has seen my brother, knows my brother or has seen his wife or their kids."

It is understood the family are on their way to New Zealand to be with Jesse in hospital.

MISSING ADELAIDE MOTHER FOUND ALIVE:

Lisa Hosking and 15-year-old Zoe Hosking. Photo / Supplied
Lisa Hosking and 15-year-old Zoe Hosking. Photo / Supplied

Yesterday an Adelaide woman reported missing after the eruption of White Island was found alive in hospital with severe burns, but the whereabouts of her daughter and husband are still unknown.

Lisa Hosking was on a two-week Royal Caribbean cruise around New Zealand with her husband Gavin, 53, and 15-year-old daughter Zoe when White Island erupted on Monday afternoon.

A family spokesman confirmed to ABC news that Lisa Hosking was alive but is in Hamilton hospital with severe burns.

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Gavin's father Brian Dallow said the hardest part of the ordeal was not knowing if his family was injured or alive.

"We've got no idea what's going on," he said.

"If we knew one way or the other I think it'd be better than trying to cling onto hope."

Zeus school, St Aloysius College, earlier released a statement confirming that Year 9 student Zoe was definitely among the missing, although information was scant.

"Our thoughts and prayers are with Zoe and her family," the school says.

"We know that you share our sadness at this time. We turn to our loving God to give us strength and courage in the days ahead."

The family was due to head to Wellington on the cruise, before docking in Sydney on December 16.