अतिपरवलय `7y^(2)-9x^(2)+54x=28y+116` की उत्केन्द्रता ज्ञात कीजिए |

Explanation

दिया गया अतिपरवलय है :
`7y^(2)-9x^(2)+54x-28y=116`
`implies(7y^(2)-28y)-(9x^(2)-54x)=116`
`implies7(y^(2)-4y)-9(x^(2)-6x)=116`
`implies7(y^(2)-2.y.2+2^(2)-4)-9(x^(2)-2.x.3+3^(2)-9)=116`
`implies7(y-2)^(2)-28-9(x-3)^(2)+81=116`
`implies7(y-2)^(2)-9(x-3)^(2)=63`
`implies((y-2)^(2))/(3^(2))-((x-3)^(2))/((sqrt(7))^(2))=1`
`implies((x-3)^(2))/((sqrt(7))^(2))-((y-2)^(2))/(3^(2))=-1`
उत्केन्द्रता, `" "a^(2)=b^(2)(e^(2)-1)`
यहाँ, `a^(2)=7` तथा `b^(2)=9`
`:." "7=9(e^(2)-1)`
या `" "(7)/(9)=(e^(2)-1)`
या `" "e^(2)=(7)/(9)+1=(16)/(9)" या "e=(4)/(3)`.