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Curves C1:x^(2)+y^(2)=r^(2) and C2:x^(2)...

Curves `C_1:x^(2)+y^(2)=r^(2) and C_2:x^(2)/16+y^(2)/9=1` intersect at four distinct points A,B,C and D. Their common tangents from a parallelogram PQRS. Q. If ABCD is sqyare, then the value of `25r^(2)` is

A

`sqrt(120)`

B

`sqrt(12)`

C

`sqrt(15)`

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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