यदि `e_(1), e_(2)` क्रमश: दीर्घवृत्त `9x^(2) + 4y^(2) = 36` तथा अतिपरवलय `9x^(2) - 4y^(2) = 36` की उत्केंद्रताएँ है, तब

Options

A. `e_(1)^(2) + e_(2)^(2) gt 3`
B. `e_(1)^(2) + e_(2)^(2) = 2`
C. `e_(1)^(2) + e_(2)^(2) gt 4`
D. `e_(1)^(2) + e_(2)^(2) lt 3`

Answer

A

Explanation

`(x^(2))/(4) + (y^(2))/(9) = 1, (x^(2))/(4) - (y^(2))/(9) = 1`
Y-अक्ष के सापेक्ष दीर्घ अक्ष `a_(1)^(2) = 9, b_(1)^(2) = 4`
X-अक्ष के सापेक्ष अनुप्रस्थ अक्ष `a_(2)^(2) = 4, b_(2)^(2) = 9`
`e_(1)^(2) = 1 - (b_(1)^(2))/(a_(1)^(2)) = 1 - (4)/(9) = (5)/(9)`,
`e_(2)^(2) = 1 + (b_(2)^(2))/(a_(2)^(2)) =1 + (9)/(4) = (13)/(4)`
`e_(1)^(2) + e_(2)^(2) = (5)/(9) + (13)/(4) = (137)/(36) gt 3` परन्तु `lt 4`