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Brums [2.3K]
1 year ago
6

NO LINKS!! Please help me with this problem​

Mathematics
2 answers:
Vinil7 [7]1 year ago
7 0

Answer:

\dfrac{y^2}{36}-\dfrac{x^2}{16}=1

Step-by-step explanation:

<u>Standard form equation of a vertical hyperbola</u>

\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1

where:

  • center = (h, k)
  • vertices = (h, k±a)
  • co-vertices = (h±b, k)
  • foci = (h, k±c) where c² = a² + b²
  • \textsf{asymptotes}: \quad y =k \pm \left(\dfrac{a}{b}\right)(x-h)
  • Transverse axis: x = h
  • Conjugate axis: y = k

From inspection of the graph:

  • center = (0, 0)  ⇒ h = 0, k = 0
  • vertices = (0, 6) and (0, -6)  ⇒  a = 6
  • co-vertices = (4, 0) and (-4, 0)  ⇒  b = 4

Substitute the found values into the formula:

\implies \dfrac{(y-0)^2}{6^2}-\dfrac{(x-0)^2}{4^2}=1

\implies \dfrac{y^2}{36}-\dfrac{x^2}{16}=1

iogann1982 [59]1 year ago
5 0

{\qquad\qquad\huge\underline{{\sf Answer}}}

The given figure shows a vertical hyperbola with its centre at origin, and as we observe the figure, we can conclude that :

Length of transverse axis is :

\qquad \sf  \dashrightarrow \: 2b = 12

\qquad \sf  \dashrightarrow \: b = 6

length of conjugate axis is :

\qquad \sf  \dashrightarrow \: 2a = 8

\qquad \sf  \dashrightarrow \: a = 4

Equation of hyperbola ~

\qquad \sf  \dashrightarrow \:    \cfrac{ {y}^{2} }{ {b}^{2} } - \cfrac{  {x}^{2} }{ {a}^{2} }  = 1

plug in the values ~

\qquad \sf  \dashrightarrow \:    \cfrac{ {y}^{2} }{ {6}^{2} } - \cfrac{  {x}^{2} }{ {4}^{2} }  = 1

\qquad \sf  \dashrightarrow \:    \cfrac{ {y}^{2} }{ {36}^{} } - \cfrac{  {x}^{2} }{ {16}^{} }  = 1

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