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Find the condition that the curves 2x=y^...

Find the condition that the curves `2x=y^(2)` and 2xy = k intersect orthogonally.

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The correct Answer is:
`k=2sqrt(2)`
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KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (SHORT ANSWER TYPE QUESTIONS)
  1. Find an angle theta, where 0 lt theta lt (pi)/(2) which increases twic...

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  2. Find the approximate value of (1.999)^(5).

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  3. Find the approximate volume of metal in a hollow spherical shell whose...

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  4. A man, 2m tall, walks at the rate of 1(2)/(3) m/s towards a street lig...

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  5. A swimming pool is to be drained for cleaning. If L represents the num...

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  6. The volume of a cube increases at a consant rate. Prove that the incre...

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  7. x and y are the sides of two squares such that y=x-x^(2). Find the rat...

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  8. Find the condition that the curves 2x=y^(2) and 2xy = k intersect orth...

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  9. Show that the curves xy=a^(2) and x^(2)+y^(2)=2a^(2) touch each other.

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  10. Find the co-ordinates of the point on the curve sqrt(x)+sqrt(y)=4 at w...

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

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  12. Prove that the curves y^(2)=4x and x^(2)+y^(2)-6x+1=0 touch each other...

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  13. Find the equation of the normal lines to the curve 3x^(2)-y^(2)=8 whic...

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  14. At what points on the curve x^(2)+y^(2)-2x-4y+1=0, the tangents are pa...

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  15. Show that a point at which the line (x)/(a)+(y)/(b)=1 touches to the c...

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  16. Show that f(x)=2x+cot^(-1)x+log(sqrt(1+x^(2))-x) is increasing in R.

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  17. Show that for a ge 1, f(x)=sqrt(3)sin x - cos x - 2ax + b is decreasin...

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  18. Show that f(x)=tan^(-1)(sin x + cos x) is an increasing function in (0...

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  19. At what point, the slope of the curve y=-x^(3)+3x^(2)+9x-27 is maximum...

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  20. Prove that f(x)=sin x+3^(1/2) cos x has maximum value at x=(pi)/(6)

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