Given an equation find the vertices, center and foci of hyperbola

Learn how to graph hyperbolas. To graph a hyperbola from the equation, we first express the equation in the standard form, that is in the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2 / b^2 = 1 for vertical hyperbola.

Next, we identify the characteristics of the given hyperbola. 'a' (the distance from the center to the vertices) is the square root of the first denominator and 'b' (the distance from the center to the covertices) is the square root of the second denominator. 'c' (the distance from the center to the foci) is obtained by taking the square root of the sum of a^2 and b^2. Using these characteristics of the hyperbola, we can graph the asymptotes of the hyperbola and hence graph the hyperbola.

Note that a hyperbola is vertical when it is facing up and down and is horizontal when it is facing right and left.
#conicsections #hyperbolaconicsections
#conicsections #hyperbolaconicsections
#conicsections #hyperbolaconicsections

[jstormtrkr]

Just wanted to drop by and say i love your videos, they help me out so much with my math when i am stuck. I find so many ah ha moments. I wish i had you for a teacher

[farjadraza]

That was the question I was trying to understand but couldn't .Thank you so much it was very informative

[ugnevucianyte]

isnt the foci formula a^2-b^2 equals c squared instead of the plus you used for the foci formula?

[ej]

I have a question what if the equation would be 9x^2-4y^2=1 how would you solve that?

[CreoleGuh]

Thank You! i am currently doing homework on this