The angle between the curves y^2 = x and x^2 = y at (1,1) is
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heya!!
x = 1 and y = 1
Angle between two curves is equal to the angle between their tangents.
let that angle be #
y² = x
differentiate w.r.t. x
2y dy / dx = 1
dy / dx. = 1 / 2y
dy / dy = 1 / 2
x² = y
differentiate w.r.t x
2x = dy / dx
dy / dx. = 2x
d'y / d'x = 2
Angle between them is
Tan ( # ) = ( 2 - 1 / 2 ) / 2
Tan ( # ) = 3 / 4
# = arc Tan ( 3 / 4 )
Have a great day ahead.
x = 1 and y = 1
Angle between two curves is equal to the angle between their tangents.
let that angle be #
y² = x
differentiate w.r.t. x
2y dy / dx = 1
dy / dx. = 1 / 2y
dy / dy = 1 / 2
x² = y
differentiate w.r.t x
2x = dy / dx
dy / dx. = 2x
d'y / d'x = 2
Angle between them is
Tan ( # ) = ( 2 - 1 / 2 ) / 2
Tan ( # ) = 3 / 4
# = arc Tan ( 3 / 4 )
Have a great day ahead.
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