Find dy/dx if 3x^3+6hx^2 y+by^3+5gx+2fy^2+2=0
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Solution:-
x2+y2+2gx+2fy+2hxy+c=0
Differentiating the given equation w.r.t. x, we have
2x+2ydxdy+2g+2fdxdy+2h((1×y)+xdxdy)+0=0
⇒(2x+2g+2hy)+dxdy(2y+2f+2hx)=0
⇒dxdy=(2y+2f+2hc)−(2x+2g+2hy)
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