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The range of parameter ' a ' for which t...

The range of parameter `' a '` for which the variable line `y=2x+a` lies between the circles `x^2+y^2-2x-2y+1=0` and `x^2+y^2-16 x-2y+61=0` without intersecting or touching either circle is `a in (2sqrt(5)-15 ,0)` `a in (-oo,2sqrt(5)-15 ,)` `a in (0,-sqrt(5)-10)` (d) `a in (-sqrt(5)-1,oo)`

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To solve the problem, we need to determine the range of the parameter \( a \) for which the line \( y = 2x + a \) lies between the two given circles without intersecting or touching either of them. ### Step 1: Write the equations of the circles in standard form. The first circle is given by: \[ x^2 + y^2 - 2x - 2y + 1 = 0 \] ...
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