0 votes 0 votes Consider the family $\mathcal{F}$ of curves in the plane given by $x=cy^2$, where $c$ is a real parameter. Let $\mathcal{G}$ be the family of curves having the following property: every member of $\mathcal{G}$ intersect each member of $\mathcal{F}$ orthogonally. Then $\mathcal{G}$ is given by $xy=k$ $x^2+y^2=k^2$ $y^2+2x^2=k^2$ $x^2-y^2+2yk=k^2$ Geometry isi2015-mma curves + – Arjun asked Sep 23, 2019 • recategorized Nov 17, 2019 by Lakshman Bhaiya Arjun 497 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes lnx = lnc + 2lny 1/x = 2/y * dy/dx dy/dx = y/2x dy/dx for orthogonal curve = - 2x/y This is true for curve (C) as can be seen by differentiation as under y^2 +2x^2 = k^2 2y dy/dx + 4x = 0 dy/dx = - 2x/y Answer: (C). Amartya answered May 18, 2020 Amartya comment Share Follow See all 0 reply Please log in or register to add a comment.