Question

The locus of the point of intersection of the two tangents drawn to the circle `x^2 + y^2=a^2` which include are angle ` alpha` is

Answer 1

`a/x=tanalpha/2`
`x=acotalpha/2`
`OB^2=AB^2+OA^2`
`(sqrt((h-0)^2+(k-0)^2))^2=sqrt(a^2cot^2alpha/2+a^2)`
`(h^2+k^2)=a^2(cot^2alpha/2+1)`
`h^2+k^2=a^2cosec^2alpha/2`
`x^2+y^2=a^2cosec^2alpha/2`