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Sagot :
Answer:
[tex] \huge\boxed{ \red{ \boxed{ \tt{ \frac{ {y}^{2} }{ {10}^{2} } - \frac{ {x}^{2} }{ {12}^{2} } = 1}}}}[/tex]
Step-by-step explanation:
to understand this
you need to know about:
- conic sections
- PEMDAS
tips and formulas:
- [tex] \sf hyperbola \:equation : \\ \sf \frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
- vertices of hyperbola:(±a,0) and (0,±b) if reversed
- [tex] \sf \: asymptotes : \\ y = \pm\frac{b}{a} x[/tex]
given:
- vertices: (0,±10)
- the hyperbola equation is inversed since the vertices is (0,±10)
- asymptotes:[tex]\pm \frac{5}{6}x[/tex]
let's solve:
- the asymptotes are in simplest and we know b is ±10
according to the question
- [tex]y = \sf \frac{5 \times 2}{6 \times 2} x \\ y = \frac{10}{12} x[/tex]
therefore we got
- a=12
- b=10
note: the equation will be inversed
let's create the equation:
- [tex] \sf substitute \: the \: value \: of \: a \: and \: b : \\ \sf \frac{ {y}^{2} }{ {10}^{2} } - \frac{ {x}^{2} }{ {12}^{2} } = 1[/tex]
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