Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Hey Mahfia, please help! Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at
y = ± [tex]\frac{5}{6} x[/tex]

Sagot :

Nayefx

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

  1. [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:

  1. [tex] \sf substitute \: the \: value \: of \: a \: and \: b : \\ \sf \frac{ {y}^{2} }{ {10}^{2} } - \frac{ {x}^{2} }{ {12}^{2} } = 1[/tex]
View image Nayefx
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.