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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 the ratio of the area of circle `C_(1)` to the area of circumcircle of `DeltaA'B'C'` is

A

`9//16`

B

`3//4`

C

`1//2`

D

none of these

Text Solution

AI Generated Solution

To solve the problem step-by-step, we need to find the ratio of the area of circle \( C_1 \) to the area of the circumcircle of triangle \( \Delta A'B'C' \). ### Step 1: Identify the equations of the circles The equations given are: - Circle \( C_1: x^2 + y^2 = r^2 \) - Ellipse \( C_2: \frac{x^2}{16} + \frac{y^2}{9} = 1 \) ### Step 2: Substitute and simplify ...
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