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If a and c are positive real number and ellipse `x^2/(4c^2)+y^2/c^2=1` has four distinct points in comman with the circle `x^2+y^2=9a^2`, then (A) `6ac+9a^2-2c^2 gt 0` (B) `6ac+9a^2-2c^2 lt 0` (C) `6ac-9a^2-2c^2 gt 0` (D) `6ac-9a^2-2c^2 lt 0`

Text Solution

Verified by Experts

2C>3a>C
`4C^2>9a^2>c^2`
`6ac+9a^2-2c^2=y`
`c(6a-c)lty<2c(3a+c)`
`6c^2>9a^2+2c^2>3c^2`
`9ac-9a^2-2c^2=Z`
`9ac-(9a^2+2c^2)=z`
`9ac-6c^2ltz<90c-3c^2`
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