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

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

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KUMAR PRAKASHAN-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 tange...

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  3. Find the equations of the tangent and normal to the given curves at th...

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  4. Find the equations of the tangent and normal to the given curves at th...

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  5. Find the equations of the tangent and normal to the given curves at th...

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  6. Find the equations of the tangent and normal to the given curves at th...

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  7. Find the equations of the tangent and normal to the given curves at th...

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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 point where x =...

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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 tangen...

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

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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 are p...

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

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

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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 pa...

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