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Find the orthogonal trajectories for the given family of curves when ‘a’ is the parameter (i) y=ax^2 (ii) cos y =ae^-x (iii) x^k +y^k =a^k (iv) Find the isogonal trajectories for the family of rectangular hyperbolas x^2 – y^2 = a^2 which makes with it an angle of 45^@.

Answer»


Answer :`(i) x^2 +2y^2 =C, (ii) siny = ce^-x, (iii) y= CX if k =2 and 1/x^k-2 - 1/ y^k-2 = 1/c^k-2 if k NE 2 (IV) x^2 - y^2 +2xy = c; x^2 - y^2 -2xy =c`


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