LOS ANGELES — The problem with sticking around as long as Betty White has is that you outlive so many of the relationships that made you happiest, like the one she had with Gita. It remains large — mammoth might be the better word — in her memory.

“Gita knew me very, very well,” White recalled recently. “We were great friends.”

She would talk and talk. Gita would listen and listen, or at least manage a convincing impression of that. And sometimes, just to make Gita happy, White would tell her to open her mouth and would “slap her tongue just as hard as I could,” she said, her voice trilling with delight. “Oh, she just thought that was wonderful.” It’s a thing with elephants. Every species gets its jollies a different way.

Gita was nearing 50 when she went five years ago to that great poacher-free savanna in the sky. White hit 89 in January and appears to be staying put, a marvel of unflagging energy and a show-business anomaly. For her, sticking around has also had an improbable advantage: She has grown busier and more widely beloved on the far side of 85. Old age hasn’t diminished her. It has given her a second wind.

She stars in “Hot in Cleveland,” a surprise hit on TV Land that was just renewed for a third season. Come fall she is slated to host an NBC reality show, tentatively titled “Betty White’s Off Their Rockers,” in which elderly people play pranks on younger ones.

And she has a new memoir of sorts, “If You Ask Me (And Of Course You Won’t),” which will reach stores Tuesday. Publishers were clamoring to get in on the Betty White Moment, and G.P. Putnam’s Sons gave her a seven-figure advance for two books, this one being the first, even though she had written a few autobiographies before.

We met on a sunny Sunday morning in mid-April at the Los Angeles Zoo, which prompted her reminiscence about Gita. The zoo is less than a half-hour’s drive from her house and, she said, her home away from home. She sits on its board of directors, has raised millions of dollars for it and is allowed to drop by outside normal hours and even mingle with the animals. So we showed up before it opened and chatted among the koalas, which she petted; the baby pronghorns, which she bottle-fed milk; and, yes, the elephants, two of which, Tina and Jewel, she tossed carrots to. Neither has ever been able to replace the wrinkly, lumbering, tongue-tickled Gita.

With Gita, “it went beyond food,” White said. “And if I’m lying to myself, I’m just going to keep lying.” She has always accentuated the positive, a disposition reflected in a face that’s all smile and a voice that’s mostly lilt. There’s a twinkle to her. A wholesomeness.

And what she has done, particularly in recent years, is play off of and against that — to hilarious effect. Accepting a lifetime achievement award from the Screen Actors Guild last year, she told the audience, “I’ve worked with quite a few” of you, then added: “Maybe had a couple. And you know who you are.” At the podium afterward George Clooney thanked her for her discretion.

And of course there was her May 2010 appearance on “Saturday Night Live,” which she hosted after hundreds of thousands of fans signed onto a Facebook campaign demanding it. One skit hinged in its entirety on her bawdy double entendres about her muffin. She won a seventh Emmy for her efforts.