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Show that x^3-3x y^2=-2 and 3x^2\ y-y^3=...

Show that `x^3-3x y^2=-2` and `3x^2\ y-y^3=2` intersect orthogonally:

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Let the given curves intersect at `(x_{1}, y_{1})`
`x^{3}-3 x y^{2}=-2 . . text { (1) } `
`3 x^{2} y-y^{3}=2 ldots(2)`
Differentiating `(1)` w.r.t.`x`,
...
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RD SHARMA-TANGENTS AND NORMALS-Solved Examples And Exercises
  1. Find the angle of intersection of curve y=4-x^2 and y=x^2

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  2. Show that y=x^3 and 6y=7-x^2 intersect orthogonally:

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  3. Show that x^3-3x y^2=-2 and 3x^2\ y-y^3=2 intersect orthogonally:

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  4. Show that x^2+4y^2=8 and x^2-2y^2=4 intersect orthogonally

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  5. Show that x^2=4y and 4y+x^2=8 intersect orthogonally at (2,\ 1)

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  6. Show that x^2=y and x^3+6y=7 intersect orthogonally at (1,\ 1)

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  7. Show that y^2=8x and 2x^2+y^2=10 at (1,\ 2sqrt(2))

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  8. Show that the curves 4x=y^2 and 4x y=k cut at right angles, if k^2=...

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  9. Show that the curves 2x=y^2 and 2x y=k cut at right angles, if k^2=...

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  10. Prove that the curves x y=4 and x^2+y^2=8 touch each other.

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  11. Prove that the curves y^2=4x and x^2+y^2-6x+1=0 touch each other at th...

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  12. Find the condition for the following set of curves to intersect ort...

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  13. Find the condition for the two concentric ellipses a1x^2+\ b1y^2=1\...

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  14. If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^...

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  15. Find the point on the curve y=x^2-2x+3 , where the tangent is pa...

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  16. Find the slope of the tangent to the curve x=t^2+3t-8 , y=2t^2-2t-5...

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  17. If the tangent line at a point (x ,\ y) on the curve y=f(x) is para...

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  18. Write the value of (dy)/(dx) , if the normal to the curve y=f(x) at...

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  19. If the tangent to a curve at a point (x ,\ y) is equally inclined t...

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  20. If the tangent line at a point (x ,\ y) on the curve y=f(x) is para...

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