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

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

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To show that the curves \(xy = a^2\) and \(x^2 + y^2 = 2a^2\) touch each other, we need to follow these steps: ### Step 1: Find the derivatives of both curves **For the first curve \(xy = a^2\):** We can use implicit differentiation. Differentiating both sides with respect to \(x\): ...
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RD SHARMA-TANGENTS AND NORMALS-Solved Examples And Exercises
  1. Show that the curves x=y^2 and x y=k cut at right angles, if 8k^2=1...

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  2. Find the value of p for which curves x^2=9p(9-y) and x^2=p(y+1) cut ea...

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  3. Show that the curves x y=a^2 and x^2+y^2=2a^2 touch each other.

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  4. Show the condition that the curves a x^2+b y^2=1 and a^(prime)\ x^2+...

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  5. If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^...

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  6. Show that the angle between the tangent at any point P and the line...

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  7. Find the angle of intersection of the curves y^2=xandx^2=y

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  8. Find the angle of intersection of curve y=x^2 and x^2+y^2=20

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  9. Find the angle of intersection of curve 2y^2=x^3 and y^2=32 x

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

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  11. Find the angle of intersection of curve (x^2)/(a^2)+(y^2)/(b^2)=1 a...

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  12. Find the angle of intersection of curve x^2+4y^2=8 and x^2-2y^2=2

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  13. Find the angle of intersection of curve x^2=27 y and y^2=8x

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  14. Find the angle of intersection of curve x^2+y^2=2x and y^2=x

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  15. Find the angle of intersection of curve y=4-x^2 and y=x^2

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  16. Show that y=x^3 and 6y=7-x^2 intersect orthogonally:

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  17. Show that x^3-3x y^2=-2 and 3x^2\ y-y^3=2 intersect orthogonally:

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  18. Show that x^2+4y^2=8 and x^2-2y^2=4 intersect orthogonally

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  19. Show that x^2=4y and 4y+x^2=8 intersect orthogonally at (2,\ 1)

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  20. Show that x^2=y and x^3+6y=7 intersect orthogonally at (1,\ 1)

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