(Actually, there is a series of such photos. The one referred to above was published by DPD on January 9, the anniversary of Richard Nixon's birth. The one below is another good angle of the King shaking hands with the President.)
"On December 21, 1970, Elvis Presley paid a visit to President Richard M. Nixon at the White House in Washington, D.C. The meeting was initiated by Presley, who wrote Nixon a six-page letter requesting a visit with the President and suggesting that he be made a 'Federal Agent-at-Large' in the Bureau of Narcotics and Dangerous Drugs..."