1didnt get properly...for chking orthogonal we replace dy/dx by -dx/dy....rit????
SOLVE DEM OR GIVE HINT
1. prove that the family of curves 
is SELF orthogonal
-
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7 Answers
62Take the point of intersection to be x1, x2
\frac{x^2}{a^2+\lambda_1}-\frac{x^2}{a^2+\lambda_1}=\lambda_1-\lambda_2
Or take a parametric form
solve for x..
Now,
\\\frac{x^2}{a^2+\lambda_1}+\frac{y^2}{b^2+1}=\lambda_1 \\\frac{2x}{a^2+\lambda_1}+\frac{2y\times\frac{dy}{dx}}{b^2+1}=0 \\\frac{dy}{dx}=-\frac{x(b^2+1)}{y(a^2+\lambda_1)}
You have to show that the product of both the solpes give -1
Which apparantly (without acutally solving) seems to be true from here..
just verify
162I thought what you were asking is that the curves or this family are orthogonal to each other...
on the other hand what you are saying is to find a family of curves orthogonal to this family of curves..
1yes if it is self orthogonal then we must get the same curve as answer wen we replace dy/dx by -dx/dy and solve it?????????
19the differential equation for the system of conics is {x + y(dy/dx)}{x-y(dy/dx)} = a2-b2