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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 parellelogram A'B'C'D'. if A'B'C'D' is a square, then r is equal to

A

`sqrt(120)`

B

`sqrt(12)`

C

`5/sqrt(2)`

D

none of these

Text Solution

Verified by Experts

Tangent of slope m to the circle and ellipse are, respectively,
`y=mx+-sqrt(r^(2)m^(2)+r^(2))`
and `y=mx+-sqrt(16m^(2)+9)`
For common tangent,
`r^(2)m^(2)+r^(2)16m^(2)+9`
Also, if A',B',C', and D' is squre, then
`m=+-`
`or r^(2)+r^(2)=25`
or `r=(5)/(sqrt(2))`
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