Question

please its urgent for me

Answer 1

Hi Mate!!!

Two curves cuts at right angles when product of their slopes = -1

Slope of ist curve x = y²

Differentiate both sides w.r.t x

2 dy/dx = 1/y

dy / dx = 1/2y. .....Slope of ist curve


Slope of second curve


xy = k


Differentiate both sides w.r.t x

dy" / dx"= -k / x²......slope of second curve.



(dy / dx )×( dy" / dx) = ( 1 / 2y ) ( -k / x²)

= -k / 2 x ( xy)

= - k / 2x ( k )

= { -1 / 2x }..... equation 1



Now solve both the given equation

x = y². and. xy = {1/2√2}


We get x = 1/2


Now put x = 1/2. in equation 1


(dy/ dx) × ( dy" / dx" ) = -1


Which shows two curves intersect at right angles.