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scheitelpunkte (-3x^2-2x+6)/5

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4x²−9y²−48x−72y+108=0

Solution

(h, k)=(6, −4), a=2√3, b=3√3

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4x²−9y²−48x−72y+108=0

Hyperbola standard equation

(y−k)²a² −(x−h)²b² =1 is the standard equation for an up-down facing hyperbola
with center (h, k), semi-axis a and semi-conjugate-axis b.

Rewrite 4x²−9y²−48x−72y+108=0 in the form of a standard hyperbola equation

(y−(−4))²(2√3)² −(x−6)²(3√3)² =1

Therefore Hyperbola properties are:

(h, k)=(6, −4), a=2√3, b=3√3

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

scheitelpunkte (-3x^2-2x+6)/5

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