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Prove that the curves x = y^(2) and xy =...

Prove that the curves `x = y^(2)` and xy = k cut at right angles* if `8k^(2) = 1`.

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NCERT TAMIL-APPLICATION OF DERIVATIVES-EXERCISE 6.3
  1. Find the equations of all lines having slope 0 which are tangent to th...

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  2. Find points on the curve (x^(2))/(9) +(y^(2))/(16) =1 at which the tan...

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  3. Find the equations of the tangent to the given curves at the indicated...

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  4. Find the equations of the tangent to the given curves at the indicated...

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  5. Find the equations of the tangent to the given curves at the indicated...

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  6. Find the equations of the tangent to the given curves at the indicated...

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  7. Find the equations of the tangent to the given curves at the indicated...

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  8. Find the equation of the tangent line to the curve y = x^(2) – 2x +7 w...

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  9. Show that the tangents to the curve y = 7x^(3) + 11 at the points wher...

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  10. Find the points on the curve y = x 3 at which the slope of the tangent...

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  11. For the curve y = 4x^(3) – 2x^(5) , find all the points at which the t...

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  12. Find the points on the curve x^(2) + y^(2) – 2x – 3 = 0 at which the t...

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  13. Find the equation of the normal at the point (am^(2) ,am^(3) ) for the...

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  14. Find the equation of the normals to the curve y = x^(3) + 2x + 6 which...

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  15. Find the equations of the tangent and normal to the parabola y^(2) = 4...

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  16. Prove that the curves x = y^(2) and xy = k cut at right angles* if 8k^...

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  17. Find the equations of the tangent and normal to the hyperbola (x^(2))/...

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  18. Find the equation of the tangent to the curve y= sqrt(3x-2) which is p...

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  19. The slope of the normal to the curve y = 2x^(2) + 3 sin x at x = 0 is

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  20. The line y = x + 1 is a tangent to the curve y^(2) = 4x at the poin

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