Question: Are the genera Tetratheca and Hyacinth in the same botanical family?

Context paragraphs:
Hyacinth (plant): Hyacinthus is a small genus of bulbous, fragrant flowering plants in the family Asparagaceae, subfamily Scilloideae.  These are commonly called hyacinths .  The genus is native to the eastern Mediterranean (from the south of Turkey through to northern Israel).

Muscari macrocarpum: Muscari macrocarpum is a perennial bulbous plant, one of a number of species and genera known as Grape Hyacinth, in this case Yellow Grape Hyacinth.  Originally from eastern Crete, Amorgos and south-west Turkey, where it grows in rocky places, it is sometimes grown as an ornamental plant.

Keeping Up Appearances: Keeping Up Appearances is a British sitcom created and written by Roy Clarke for the BBC, centred on the life of eccentric and snobbish middle class social climber Hyacinth Bucket, who insists that her surname is pronounced "Bouquet".  The sitcom follows Hyacinth in her attempts to prove her social superiority and to gain standing with those she considers upper class; attempts that are constantly hampered by her decidedly lower class extended family whom she desperately seeks to hide.  Much of the humour comes from the culture clash between Hyacinth's vision of herself and the reality of her working-class background, plus the farcical situations in which she finds herself as she battles to protect her social credibility.

Muscari armeniacum: Muscari armeniacum is a bulbous plant of the genus "Muscari" with basal, simple leaves and short, flowering stems.  It is one of a number of species and genera known as grape hyacinth, in this case Armenian grape hyacinth or Garden Grape-hyacinth.  The flowers are purple, blue (with a white fringe), white (var.  "Album") or pale pink (var "Pink Sunrise") and the plants are usually 15 cm tall.  "M. armeniacum" blooms in mid-Spring (April or May in the Northern Hemisphere) for 3–4 weeks.  Some selections are fragrant.  Established bulbs leaf in the autumn.

Tetratheca: Tetratheca is a genus of around 50 to 60 species of shrubs endemic to Australia.  It is classified in the botanical family Elaeocarpaceae, now known to encompass the family Tremandraceae, which the genus originally belonged to.  It occurs throughout extratropical Australia, and has been recorded in every mainland state except the Northern Territory.

Tremandraceae: Tremandraceae R.Br.  ex DC.  is the name of a defunct family of flowering plants.  It contained three genera: "Platytheca", "Tetratheca", and "Tremandra".  In 2006, a molecular phylogenetic study showed that Tremandraceae is embedded in Elaeocarpaceae.  Recognizing Tremandraceae as a separate family would make Elaeocarpaceae paraphyletic.

Leopoldia comosa: Leopoldia comosa (syn.  Muscari comosum) is a perennial bulbous plant.  Usually called the tassel hyacinth or tassel grape hyacinth, it is one of a number of species and genera also known as grape hyacinths.  It is found in rocky ground and cultivated areas, such as cornfields and vineyards, in south-east Europe to Turkey and Iran, but has naturalized elsewhere.  In southern Italy, Portugal and Greece, its bulb is a culinary delicacy.

Muscari neglectum: Muscari neglectum is a perennial bulbous plant, one of a number of species and genera known as grape hyacinth and in particular common grape hyacinth or starch grape hyacinth. " Muscari" are perennial bulbous plants native to Eurasia.  They produce spikes of dense, commonly blue, urn-shaped flowers.  It is sometimes grown as an ornamental plant, for example, in temperate climates as a spring bulb.

Arecaceae: The Arecaceae are a botanical family of perennial climbers, shrubs, acaules and trees commonly known as palm trees (owing to historical usage, the family is alternatively called Palmae).  They are flowering plants, a family in the monocot order Arecales.  Currently 181 genera with around 2600 species are known, most of them restricted to tropical and subtropical climates.  Most palms are distinguished by their large, compound, evergreen leaves, known as fronds, arranged at the top of an unbranched stem.  However, palms exhibit an enormous diversity in physical characteristics and inhabit nearly every type of habitat within their range, from rainforests to deserts.

List of Arecaceae genera: This is a list of all the genera in the botanical family Arecaceae, the palm tree family, arranged by tribes within the family.

Supporting paragraphs: Tetratheca Hyacinth (plant)
Answer: no