Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the center of the hyperbola 9x2−y2−81=09x^2 - y^2 - 81 = 0?\newline(_,_)(\_,\_)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Find properties of hyperbolas from equations in general formright chevron icon

Full solution

Q. What is the center of the hyperbola 9x2−y2−81=09x^2 - y^2 - 81 = 0?\newline(_,_)(\_,\_)
  1. Write Equation: Write down the given equation of the hyperbola.\newlineThe given equation is 9x2−y2−81=09x^2 - y^2 - 81 = 0.
  2. Move Constant: Move the constant term to the right side of the equation.\newline9x2−y2=819x^2 - y^2 = 81
  3. Divide by 8181: Divide both sides of the equation by 8181 to get the equation in standard form.\newline(9x2)/81−(y2)/81=81/81(9x^2)/81 - (y^2)/81 = 81/81\newlineSimplify the equation to get:\newlinex2/9−y2/81=1x^2/9 - y^2/81 = 1
  4. Simplify Equation: Identify the center of the hyperbola.\newlineThe standard form of the equation of a hyperbola is (x−h)2/a2−(y−k)2/b2=1(x-h)^2/a^2 - (y-k)^2/b^2 = 1 for a horizontal hyperbola, or (y−k)2/a2−(x−h)2/b2=1(y-k)^2/a^2 - (x-h)^2/b^2 = 1 for a vertical hyperbola, where (h,k)(h, k) is the center of the hyperbola.\newlineIn our equation x2/9−y2/81=1x^2/9 - y^2/81 = 1, we can see that it matches the form (x−h)2/a2−(y−k)2/b2=1(x-h)^2/a^2 - (y-k)^2/b^2 = 1 with h=0h = 0 and k=0k = 0.\newlineTherefore, the center of the hyperbola is at (0,0)(0, 0).

More problems from Find properties of hyperbolas from equations in general form

Question
Write the equation in standard form for the hyperbola x2−y2=64x^2 - y^2 = 64.\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the center of the hyperbola 4x2−y2−100=04x^2 - y^2 - 100 = 0?\newline(_,_)(\_,\_)
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the center of the hyperbola (x2144)−(y281)=1(\frac{x^2}{144}) - (\frac{y^2}{81}) = 1?\newline(_____,_____)
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the length of the transverse axis of the hyperbola (x264)−(y236)=1(\frac{x^2}{64}) - (\frac{y^2}{36}) = 1?\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Write the equation in standard form for the hyperbola y2−x2=81y^2 - x^2 = 81.\newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
Write the equation in standard form for the hyperbola x2−4y2=100x^2 - 4y^2 = 100.\newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
Write the equation in standard form for the hyperbola 9y2−x2=369y^2 - x^2 = 36.\newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
Write the equation in standard form for the hyperbola 4x2−y2=164x^2 - y^2 = 16.\newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
Write the equation in standard form for the hyperbola y2−9x2=144y^2 - 9x^2 = 144.\newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
The graph of y=f(x+3) y=f(x+3) is shown. For which value of x x , rounded to the nearest whole number, must f(x)=0 f(x)=0 ?
Get tutor helpright-arrow

Posted 25 days ago

View all (35)