Question

How do you graph x^2+9y^2=9?

Answer 1

x29−y21=1x29-⁢y21=1This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.(x−h)2a2−(y−k)2b2=1x-⁢h2a2-⁢y-⁢k2b2=1Match the values in this hyperbola to those of the standard form. The variable hh represents the x-offset from the origin, kk represents the y-offset from origin, aa.a=3a=3b=1b=1k=0k=0h=0h=0The center of a hyperbola follows the form of (h,k)h,k. Substitute in the values of hh and kk.(0,0)0,0Find cc, the distance from the center to a focus.
√1010Find the vertices.
(3,0),(−3,0)3,0,-3,0Find the foci..(√10,0),(−√10,0)10,0,-⁢10,0Find the eccentricity.
√103103Find the focal parameter.
√10101010The asymptotes follow the form y=±b(x−h)a+ky=±b⁢x-⁢ha+k because this hyperbola opens left and right.y=±13x+0y=±13⁢x+0Simplify to find the first asymptote.
y=x3y=x3Simplify to find the second asymptote.
y=−x3y=-⁢x3This hyperbola has two asymptotes.y=x3,y=−x3y=x3,y=-⁢x3These values represent the important values for graphing and analyzing a hyperbola.Center: (0,0)0,0Vertices: (3,0),(−3,0)3,0,-3,0Foci: (√10,0),(−√10,0)10,0,-⁢10,0Eccentricity: √103103Focal Parameter: √10101010Asymptotes: y=x3y=x3, y=−x3y=-⁢x3