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Show that the following set of curves intersect orthogonally: (i) `y=x^3 and 6y=7-x^2`, (ii) `x^3-3x y^2=-2 and 3x^2y-y^3=2.` (iii) `x^2+4y^2=8 and x^2-2y^2=4`

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RD SHARMA ENGLISH-TANGENTS AND NORMALS-All Questions
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  18. Find the equation of the normal to y=2x^3-x^2+3 at (1,4).

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