Respuesta :

The equation of the hyperbola with a given origin has vertices at (±[tex]\sqrt{61}[/tex], 0) and foci at  (±[tex]\sqrt{98}[/tex], 0) is  [tex]\frac{x^2}{61} -\frac{y^2}{37} =1[/tex].

Given, that a hyperbola centred at the origin has vertices at (±[tex]\sqrt{61}[/tex], 0) and foci at  (±[tex]\sqrt{98}[/tex], 0)

What is hyperbola?

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

The formula for a hyperbola centred at the origin is [tex]\frac{x^2}{a^2} -\frac{y^2}{b^2 } =1[/tex]

The vertices are located at (±a, 0), so we have that the value of a is [tex]\sqrt{61}[/tex].

The foci are located at (±c, 0), where [tex]c^2 = a^2 + b^2[/tex].

So if we have that [tex]c = \sqrt{98}[/tex], we can find the value of b:

[tex]98 = 61 + b^2[/tex]

⇒ [tex]b^2 = 37[/tex]

⇒ [tex]b = \sqrt{37}[/tex]

So, the formula for this hyperbola is [tex]\frac{x^2}{61} -\frac{y^2}{37} =1[/tex].

Therefore, the equation of the hyperbola with a given origin has vertices at (±[tex]\sqrt{61}[/tex], 0) and foci at  (±[tex]\sqrt{98}[/tex], 0) is  [tex]\frac{x^2}{61} -\frac{y^2}{37} =1[/tex].

To learn more about hyperbola visit:

https://brainly.com/question/27799190.

#SPJ1

ACCESS MORE
EDU ACCESS
Universidad de Mexico