The angle of intersection of the curves `y=x^(2)andx=y^(2)` at (1,1) is

Options

A. `tan^(-1)((4)/(3))`
B. `tan^(-1)(1)`
C. `90^(@)`
D. `tan^(-1)((3)/(4))`

Answer

D

Explanation

The slope of the curve
`y=x^(2)implies(dy)/(dx)=2x`
`therefore((dy)/(dx))_((1,1))=2=m_(1)`
and slope of the curve
`x=y^(2)`
`implies1=2y(dy)/(dx)`
`implies(dy)/(dx)=(1)/(2y)implies((dy)/(dx))_((1,1))=(1)/(2)=m_(2)`
`therefore` Angle of intersection at the point (1,1) is
`tantheta=(m_(1)-m_(2))/(1+m_(1)m_(2))=(2-(1)/(2))/(1+2xx(1)/(2))=(3)/(4)`
`thereforetheta=tan^(-1)(3)/(4)`