Write the equation of a hyperbola with a center at (-5, -3), vertices at (-5, -5) and (-5, -1) and co-vertices at (-11, -3) and (1, -3)

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

Write the equation of a hyperbola with a center at (-5, -3), vertices at (-5, -5) and (-5, -1) and co-vertices at (-11, -3) and (1, -3)

Algebra
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

Well, since the y-coordinate is what changes between the two vertices, this will be a hyperbola opening up and down, which means the fraction that has the y-variable will be the positive of the two fractions in the equation. So we know we have a hyperbola of this form \[\frac{ (y-k)^{2} }{ a^{2} } - \frac{ (x-h)^{2} }{ b^{2} } = 1\] The a^2 is always with the positive fraction and the b^2 is always with the negative fraction when dealing with a hyperbola. Now we are given the center (h,k) = (-5,-3). So we can plug those values in and have this now: \[\frac{ (y+3)^{2} }{ a^{2} } - \frac{ (x+5)^{2} }{ b^{2} } = 1\] Now, the denominator of the fraction with the variable x represents a distance left and right from the center while the denominator of the fraction with y in it reprsents a distance up and down from the center. Since each vertex is up 2 or down 2 from the center, this means a = 2 and thus a^2 = 4. Now I havent heard the term co-vertices used before, but I assume it just means the values that would be on the imaginary box that is normally used to sketch the asymptotes. Either way, this distance is left 6 and right 6 from the center, therefore we have b = 6 which means b^2 = 36. Thus our full equation is \[\frac{ (y+3)^{2} }{ 4 } - \frac{ (x+5)^{2} }{ 36 } = 1\]

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

1 Attachment
Well, its center is (3,2) based on the equation, so the ellipse will be symmetric about its center. So yes
@Concentrationalizing thanks how about this one
1 Attachment
Well, you need to know which denominator would give you vertices and which one would give you co-vertices. So first off, which equations are ellipses and which ones are hyperbolas?
i have no clue
Well, I explain a lot of it to ya, but there are things you will eventually have to pick up from studying and such. An ellipse has an equation of this form: \[\frac{ (x-h)^{2} }{ a^{2} } + \frac{ (y-k)^{2} }{ b^{2} } = 1\] The order of a^2 and b^2 may be flip-flopped depending on the equation A hyperbola has an equation of this form: \[\frac{ (x-h)^{2} }{ a^{2} } - \frac{ (y-k)^{2} }{ b^{2} }=1\] Which fraction contains x and which one contains y may be flip-flopped in a hyperbola So can you see which ones would be ellipses and which would be hyperbolas?

Not the answer you are looking for?

Search for more explanations.

Ask your own question