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Show that the curve xy=a^2 and x^2+y^2=2...

Show that the curve `xy=a^2` and `x^2+y^2=2a^2` touch each other.

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PATHFINDER-APPLICATION OF DERIVATIVES-QUESTION BANK
  1. At what point of the ellipes 16x^2+9y^2=400, does the ordinate decrea...

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  2. A particle moves along the curve 6y = x^(3) +2. Find the points on the...

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  3. A ladder 16 cm long is leaning against a wall. The bottom of the ladde...

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  4. Water is leaking from a conical funnel at the rate of 5 cm^3/sec. If t...

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  5. Show that f(x)=(1/2)^x is strictly decreasing on R.

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  6. Show that : tanx -x is strictly increasing on (0,pi/2).

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  7. Show that the following function is strictly increasing :f(x)=x^2,x>0.

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  8. Find the intervals on which the following function is strictly increas...

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  9. Find the intervals on which the following function is strictly increa...

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  10. Find the intervals on which the following function is strictly increa...

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  11. FInd the slopes of the tangents and normals to the following curve: x=...

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  12. Show that the tangents to the curve y=x^2-5x+6 at the point (2,0) and ...

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  13. Find the equations of the tangent and normal to the curve y=x^2-4x-5 a...

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  14. Find the equation of the tangent to the ellipse x^2/a^2+y^2/b^2=1 at (...

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

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  16. FInd the equation of the normal to the curve 3x^2-y^2=8 which is para...

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  17. Show that the curve xy=a^2 and x^2+y^2=2a^2 touch each other.

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

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  19. Find the angle of intersection of the curve x^2+y^2-4x-1=0 and x^2+y^2...

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  20. If y=x^4-10 and if x change from 2 to 1.99, what is the approximate c...

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