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C(1):x^(2)+y^(2)=r^(2)and C(2):(x^(2))/(...

`C_(1):x^(2)+y^(2)=r^(2)and C_(2):(x^(2))/(16)+(y^(2))/(9)=1` interset at four distinct points A,B,C, and D. Their common tangents form a peaallelogram A'B'C'D'.
if A'B'C'D' is a square, then r is equal to

A

`(12)/(5)sqrt(2)`

B

`(12)/(5)`

C

`(12)/(5sqrt(5))`

D

none of these

Text Solution

Verified by Experts


Solving the cruves given (eliminating `x^(2)`) , we have
`(r^(2)-y^(2))/(16)+(y^(2))/(8)=1`
or `y^(2)=(16r^(2)-144)/(7)`
If ABCD is a square, then
`x^(2)=y^(2)`
`or (144-9r^(2))/(7)=(16r^(r)-144)/(7)`
or `25r^(2)=288`
or `r=(12)/(5)sqrt(2)`
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