Finding the equation of a hyperbola

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In summary, the conversation discusses finding the equation and sketching a hyperbola with a given vertex and asymptotes. The poster has found the center and vertex, but needs to find the value of b to complete the equation. They are given the slope of the asymptotes and can use the formula a/b to solve for b.
  • #1
farmd684
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Homework Statement




Problem : Find an equation and sketch in x-y coordinates for the Hyperbola with vertex (-1,7) and asymptotes y-5=+- (x+1)

The Attempt at a Solution



To find the equation of the hyperbola i have to find the length of a ( distance from center to vertex in focal axis ) and b to put them in the equation y^2/a^2 - x^2/b^2 = 1 so far i have found the center (-1,5) and vertex are (-1,7) and (-1,3) so i get a = 2 But how can i get the value of b to put it in the equation ? Thanks :)
 
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  • #2
Hi farmd684! :smile:

(try using the X2 tag just above the Reply box :wink:)

If the question gives you lemons … make lemonade! :biggrin:

For y2/a2 - x2/b2 = 1, what is the slope of the asymptotes? :wink:
 
  • #3
tiny-tim said:
Hi farmd684! :smile:

(try using the X2 tag just above the Reply box :wink:)

If the question gives you lemons … make lemonade! :biggrin:

For y2/a2 - x2/b2 = 1, what is the slope of the asymptotes? :wink:

Thanks for the reply :biggrin:

the slope i guess is a/b for y2/x2. Then what should i do.
 
  • #4
farmd684 said:
Thanks for the reply :biggrin:

the slope i guess is a/b for y2/x2. Then what should i do.

Well, if you know a/b and you know a, then b = … ? :smile:
 
  • #5
tiny-tim said:
Well, if you know a/b and you know a, then b = … ? :smile:

Thanks :smile:
 

1. What is a hyperbola?

A hyperbola is a type of curved shape that is formed when a plane cuts through a cone at an angle. It is characterized by two distinct, curved branches that are symmetrical about a central axis.

2. How do you find the equation of a hyperbola?

The general equation for a hyperbola is (x-h)^2/a^2 - (y-k)^2/b^2 = 1, where (h,k) is the center point and a and b are the distances from the center to the vertices on the x and y axes, respectively. To find this equation, you will need to know the coordinates of the center, the distances from the center to the vertices, and the orientation of the hyperbola.

3. What is the difference between a horizontal and vertical hyperbola?

A horizontal hyperbola is one in which the two branches open to the left and right, while a vertical hyperbola is one in which the two branches open upwards and downwards. The orientation of the hyperbola will affect the values of a and b in the equation.

4. Can you graph a hyperbola without knowing its equation?

Yes, it is possible to graph a hyperbola without knowing its equation. However, you will need to know at least three points on the hyperbola, as well as the orientation (horizontal or vertical) in order to accurately plot the curve.

5. How are hyperbolas used in real life?

Hyperbolas are commonly used in architecture and engineering, as they can be used to create curved structures such as arches and bridges. They are also used in physics and astronomy to describe the orbits of celestial bodies, and in economics to model supply and demand curves.

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