Kuta Software - Infinite Algebra 2 - Eccentricity of Conic Sections - Identify the eccentricity of each

Oct 8, 2026

Uploaded by Aurelia

Worksheet for Infinite Algebra 2 on eccentricity of conic sections. Problems ask students to identify the eccentricity of each conic, including hyperbolas and ellipses, using provided geometric information such as vertices, foci, centers, and co-vertices. Additional tasks require converting given information into standard form equations for individual hyperbolas and ellipses. Suitable for practice and assessment of eccentricity concepts and conic standard forms.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

Identify the eccentricity of each

Hyperbola eccentricity problems

Ellipse eccentricity problems

Write standard form equations

Hyperbolas

Ellipses

Kuta Software-Infinite Algebra 2 Name Eccentricity of Conic Sections Date Period Identify the eccentricity of each. 2 2 2 2 1) x16 − y9~~ ~~ = 1 2) x4~~ ~~ + ~~ ~~y25 = 1 3) x = 2y 2 x2 y 2 4) 15 + 45 = 1 5) y~~ ~~216 − x 2 = 1 6) x 2 + y 2 = 4 7) (x~~ ~~2)~~ ~~2~~ ~~ + ~~ ~~(~~ ~~y~~ ~~+162)~~ ~~2~~ ~~ = 1 8) (x~~ ~~1)~~ ~~2~~ ~~ − (~~ ~~y~~ ~~2)2~~ ~~ = 1 9) (x − 4)2 + ( y − 2)2 = 1 10) y = (x − 6)2 + 3 ( y + 1) 2 x 2 x2 11) − = 1 12) + ( y + 3) 2 = 1 16 25 49 13) x 2 − 9 y 2 − 9 = 0 14) 25x 2 + 16 y 2 − 400 = 0 15) x 2 + y2 + 4x + 8y + 11 = 0 16) 4x 2 + 9 y 2 − 16x − 36 y + 16 = 0 Use the information provided to write the standard form equation of each hyperbola. 17) Vertices: ( 11, 8), (5, 8) 18) Foci: ( 19, −3), (−7, −3) Eccentricity = ~~ ~~1783~~ ~~ Eccentricity = ~~ ~~135 19) CentVerteer ax att ((9,143, )3) 20) Center at (− ~~ ~~32~~ ~~ , 8) Eccentricity = ~~ ~~615~~ ~~ Focus at (− ~~ ~~32~~ ~~ , 8 + 185 ) Eccentricity = ~~ ~~1858 Use the information provided to write the standard form equation of each ellipse. 21) Eccentricity = ~~ ~~513~~ ~~ 22) Eccentricity = ~~ ~~513 Vertices: (3, 3), (−23, 3) Foci: (−5, 4), (−5, −6) 23) Eccentricity = ~~ ~~2~~ ~~914~~ ~~ 24) Eccentricity = ~~ ~~215 Co-vertices: (0, −10), (−10, −10) Center: (−8, 8) Vertex: (2, 8) 25) Eccentricity = ~~ ~~114~~ ~~Center: (2, −9) Focus: (2, −9 − 5 ) 26) Eccentricity = ~~ ~~357 Center: (7, −4) Co-vertex: (7 + 10 , −4) Kuta Software-Infinite Algebra 2 Name___________________________________ Eccentricity of Conic Sections Date________________ Period____ Identify the eccentricity of each. 2 2 2 2 1) x16 − y9~~ ~~ = 1 2) x4~~ ~~ + ~~ ~~y25 = 1 Eccentricity: 54 = 1.25 Eccentricity: ~~ ~~215~~ ~~ ≈ 0.917 3) x = 2y 2 x2 y 2 4) ~~ ~~ + ~~ ~~ = 1 Eccentricity: 1 15 45 Eccentricity: ~~ ~~3~~ ~~ ≈ 0.816 5) y~~ ~~216 − x 2 = 1 6) x 2 + y 2 = 4 Eccentricity: 0 Eccentricity: ~~ ~~174~~ ~~ ≈ 1.031 7) (x~~ ~~2)~~ ~~2~~ ~~ + ~~ ~~(~~ ~~y~~ ~~+162)~~ ~~2~~ ~~ = 1 8) (x~~ ~~1)~~ ~~2~~ ~~ − (~~ ~~y~~ ~~2)2~~ ~~ = 1 Eccentricity: ~~ ~~2~~ ~~ ≈ 0.866 Eccentricity: ~~ ~~132~~ ~~ ≈ 1.803 9) (x − 4)2 + ( y − 2)2 = 1 10) y = (x − 6)2 + 3 Eccentricity: 0 Eccentricity: 1 11) (~~ ~~y~~ ~~+161)~~ ~~2 − x225 = 1 12) x~~ ~~249 + ( y + 3) 2 = 1 Eccentricity: ~~ ~~414~~ ~~ ≈ 1.601 Eccentricity: 4~~ ~~7~~ ~~ ≈ 0.99 13) x 2 − 9 y 2 − 9 = 0 14) 25x 2 + 16 y 2 − 400 = 0 Eccentricity: ~~ ~~103~~ ~~ ≈ 1.054 Eccentricity: ~~ ~~35 = 0.6 15) x 2 + y2 + 4x + 8y + 11 = 0 16) 4x 2 + 9 y 2 − 16x − 36 y + 16 = 0 Eccentricity: 0 5 Eccentricity: ≈ 0.745 3 Use the information provided to write the standard form equation of each hyperbola. 17) Vertices: ( 11, 8), (5, 8) 18) Foci: ( 19, −3), (−7, −3) Eccentricity = ~~ ~~1783~~ ~~ Eccentricity = ~~ ~~135 (x~~ ~~−98)~~ ~~2~~ ~~ − (~~ ~~y~~ ~~−~~ ~~8169)2~~ ~~ = 1 ~~ ~~(x~~ ~~−256)~~ ~~2~~ ~~ − (~~ ~~y~~ ~~+~~ ~~3144)2~~ ~~ = 1 19) CentVerteer ax att ((9,143, )3) 20) Center at (− ~~ ~~32~~ ~~ , 8) Eccentricity = ~~ ~~615~~ ~~ Focus at (− ~~ ~~32~~ ~~ , 8 + 185 ) (x − 9) 2 ( y − 3)2 Eccentricity = 185 25 − 36 = 1 8 ( y − 8) 2 (x + 32) 2 ~~ ~~ − ~~ ~~ = 1 64 121 Use the information provided to write the standard form equation of each ellipse. 21) Eccentricity = ~~ ~~513 Vertices: (3, 3), (−23, 3) (x + 10) 2 ( y − 3) 2 + = 1 169 144 23) Eccentricity = ~~ ~~2~~ ~~914 Co-vertices: (0, −10), (−10, −10) (x + 5) 2 ( y + 10) 2 + = 1 25 81 25) Eccentricity = ~~ ~~114~~ ~~Center: (2, −9) Focus: (2, −9 − 5 ) (x − 2) 2 ( y + 9) 2 + = 1 65 70 22) Eccentricity = ~~ ~~513 Foci: (−5, 4), (−5, −6) (x + 5) 2 ( y + 1) 2 + = 1 144 169 24) Eccentricity = ~~ ~~215 Center: (−8, 8) Vertex: (2, 8) (x + 8) 2 ( y − 8) 2 + = 1 100 16 26) Eccentricity = ~~ ~~357 Center: (7, −4) Co-vertex: (7 + 10 , −4) (x − 7) 2 ( y + 4) 2 + = 1 10 35 Create your own worksheets like this one with Infinite Algebra

FAQs

What is the main topic of this worksheet?

The worksheet focuses on eccentricity of conic sections, especially hyperbolas and ellipses.

What types of information are given for each problem?

Problems provide features like vertices, foci, centers, and co-vertices to support eccentricity calculations and standard form equations.

What do problems 17–20 ask students to do?

They use the given hyperbola information to write standard form equations and determine corresponding eccentricity values.

Oct 8, 2026

Uploaded by Aurelia