Question

`5y^(2)-9x^(2)=36`

Answer 1

Correct Answer - `(i) (12)/(sqrt(5))"units,4units"`
(ii) `A(0,-(6)/(sqrt(5))),B(0,(6)/(sqrt(5)))`
`(iii) F_(1)(0,-2sqrt((14)/(5))),F_(2)(0,2sqrt((14)/(5)))`
(iv) `e=(sqrt(14))/(3)`
(v) `(4sqrt(5))/(3) ` units
Given equation is `(y^(2))/(( 36//5))-(x^(2))/(4)=1.`
`therefore a^(2)=(36)/(5),b^(2)=4 and c^(2)=(a^(2)+b^(2))=((36)/(5)+4)=(56)/(5).`
Also `, e=( c)/(a)=((sqrt(56))/(sqrt(5))xx(sqrt(5))/(6))=(2sqrt(14))/(6)=(sqrt(14))/(3).`