Straight line `3x-4y=4/(pi)sin^(-1)(a^(8)+1)+2cos^(-1)(a^(12)+1)-sec^(-1)(a^(2)+1),aepsilonR` & `6x-8y=7` are tangents to a circle then the length of arc of this circle which makes on angle of `40/3` at its centre is

Answer

2

Explanation

For `4/(pi)sin^(-1)(a^(8)+1)+2cos^(-1)(a^(12)+1)-sec^(-1)(a^(2)+1)` to be defined `a=0`
`:. 3x-4y=4/(pi).(pi)/2+2.0-0=2`
`3x-4y=2`
`6x-5y=7`
`d=|(7/2-2)/5|=3/10`
`r=3/20`
`I=rtheta=3/20xxtheta=2`