Question

the orthogonal trajectory of the curve xy=c passing through the point (2,1) is​

Answer 1

Answer:

xy=k

2

⇒y+x

dx

dy

=0

⇒

dx

dy

=−

x

y

Replacing

dx

dy

→−

dy

dx

∴−

dy

dx

=−

x

y

⇒xdx=ydy

⇒x

2

=y

2

+c⇒x

2

−y

2

=c

Answer 2

Answer:

xy=k2⇒y+xdxdy=0

⇒dxdy=−xy

Replacing dxdy→−dydx

∴−dydx=−xy⇒xdx=ydy⇒x2=y2+c⇒x2−y2=c