Question

Let `alpha` be a variable parameter, then the length of the chord of the curve: `(x-sin^-1 alpha)(x-cos^-1 alpha)+(y-sin^-1 alpha)(y+cos^-1 alpha)=0` along the line `x=pi/4` can not be equal to

Answer 1

length=`|y_2-y_1|`
`(pi/4-sin^(-1)alpha)(pi/4-cos^(-1)alpha)+(y-sin^(-1)alpha(y+cos^(-1)alpha)=0`
`pi^2/6-pi/4(sin^(-1)alpha+cos^(-1)alpha)+y^2+(cos^(-1)alpha-sin^(-1)alpha)y=0`
`y^2+(cos^(-1)alpha-sin^(-1)alpha)y-pi^2/16=0`
`y_1+y_2=sin^(-1)alpha-cos^(-1)alpha=2sin^(-1)alpha-pi/2`
`y_1y_2=-pi^2/16`
`|y_1-y_2|=sqrt(y_1-y_2)^2` `sqrt((y_1+y_2)^2-4y_1y_2)`
`sqrt((2sin^(-1)alpha-pi/2)^2+pi^2/4)>=pi/2`
correct options are a,b,c.