Acute angle between two curve `x^(2)+y^(2)=a^(2)sqrt2` and `x^(2)-y^(2)=a^(2)` is

Options

A. `(pi)/(6)`
B. `(pi)/(3)`
C. `(pi)/(4)`
D. none of these

Answer

C

Explanation

`x^(2)+y^(2)=a^(2)sqrt2 and x^(2)-y^(2)=a^(2)`
`therefore" "(dy)/(dx)=(-x)/(y),(dy)/(dx)=(x)/(y)`
Angle between curves is given by
`theta=|tan^(-1).((x)/(y)+(x)/(y))/(1-(x^(2))/(y^(2)))|`
`=|tan^(-1).(2xy)/(y^(2)-x^(2))|`
Squaring and subtracting the equations of given curves,
`4x^(2)y^(2)=a^(4)`
`therefore" "2xy= pm a^(2)`
`therefore" "theta=|tan^(-1).(a^(2))/(a^(2))|`
`=tan^(-1)(1)`
`=(pi)/(4)`