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Show that the curve xy=a^(2)andx^(2)+y^(...

Show that the curve `xy=a^(2)andx^(2)+y^(2)=2a^(2)` touch each other.

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PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE
  1. At what point of the curve y = x^2 does the tangent make an angle of 4...

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  2. Find the equations of the tangents to the curve 3x^2 - y^2 = 2 which a...

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  3. Show that the curve xy=a^(2)andx^(2)+y^(2)=2a^(2) touch each other.

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

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  5. Prove that the curves y^2 = 4x and x^2 + y^2 - 6x + 1 = 0 touch each o...

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  6. Find the equations of normal(s) to the curve x^2 + 2y^2 - 4x - 6y + 8 ...

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  7. Find the coordinates of the point on the curve sqrtx + sqrty = 4 at wh...

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  8. Show that the equations of the normal at any point theta on the curve ...

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  9. Find the angle of intersection of the curves y=x^(2) and y=4-x^(2).

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  10. Show that the line x/a + y/b = 1 touches the curve y = be^(x//a) at th...

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

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  12. Prove that the curves x = y^2 and xy = k cut at right angles if 8k^2 =...

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  13. Find the condition that the curves 2x = y^2 and 2 xy = k may intersect...

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  14. For the curve y = 5x - 2x^3, if x increases at te rate of 2units/s, th...

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  15. In the following problems, use differentials to find the approximate v...

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  16. In the following problems, use differentials to find the approximate v...

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  17. In the following problems, use differentials to find the approximate v...

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  18. In the following problems, use differentials to find the approximate v...

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  19. In the following problems, use differentials to find the approximate v...

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  20. In the following problems, use differentials to find the approximate v...

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