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If the curves : alpha x^(2)+betay^(2)=...

If the curves :
`alpha x^(2)+betay^(2)=1 and alpha'x^(2)+beta'y^(2)=1` intersect orthogonally, prove that `(alpha-alpha')beta beta'=(beta-beta')alpha alpha'` .

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MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE 6 (c) (Long Answer Type Questions (I))
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  2. Find the equation of tangent to the curve given byx=asin^3t ,y=bcos^3t...

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  3. Find the equation of the tangent at t=(pi)/(4) to the curve : x=sin 3t...

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  4. Find the point(s) on the curve : (i) y=3x^(2)-12x+6 (ii) x^(2)+y^...

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  6. Find the point on the curve y=x^3-11 x+5 at which the tangent is y"...

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  7. For the curve y=4x^3-2x^5,find all the points at which the tangent pa...

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  8. Find the points on the following curve at which the tangents are paral...

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  9. At what point on the circle x^2+y^2-2x-4y+1=0, the tangent is parallel...

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  10. Find points on the curve (x^2)/4+(y^2)/(25)=1at which the tangents ar...

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  11. Show that the tangents to the curve y=7x^3+11 at the points x=2 and...

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  12. Find the equations of all lines having slope 0 which are tangent to t...

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  13. Find the equations of all lines : having slope -1 and that are tange...

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  14. Find the equations of all lines having slope 2 and that are tangent...

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  15. Find the point of intersection of the tangent lines to the curve y=2x^...

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  16. Prove that the tangents to the curve y=x^2-5x+6 at the points (2, 0...

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  17. Find the angle of intersection of the curves : (i) y^(2)=4x and x^(2...

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  18. Find the angle of intersection of the curves : (ii) x^(2)+y^(2)-4x-...

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  19. Show that the following set of curves intersect orthogonally: y=x^3a ...

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  20. If the curves : alpha x^(2)+betay^(2)=1 and alpha'x^(2)+beta'y^(2)=1...

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