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if the straight line xcosalpha+y sin alp...

if the straight line `xcosalpha+y sin alpha=p` touches the curve `x^my^n=a^(m+n)` prove that `p^(m+n)m^mn^n=(m+n)^(m+n) a^(m+n) sin^nalpha cos^malpha`

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A DAS GUPTA-Application of dy/dx-Exercise
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  2. Determine the quadratic curve y=f(x) if it touches the line y=x at the...

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  3. Find the value of a ,b ,c such that curves y=x^2=a x+ba n dy=c x-x^2 w...

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  4. Prove that the curves 2y^2 =x^3 and y^ 2 = 32x cut each other orthogon...

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  5. Prove that the curves x y=4a n dx^2+y^2=8 touch each other.

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  6. Find the equation of the tangent to the curve y=(x^3-1)(x-2) at the...

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  7. Show that the line d/a+y/b=1 touches the curve y=b e^(-x/a) at the poi...

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  8. The equation of tangents to the curve y=cos(x+y), -2pi le x le 2pi tha...

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  9. Find the equations of the tangents drawn to the curve y^2-2x^3-4y+8=0.

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  10. If the tangent at (x(0),y(0)) to the curve x^(3)+y^(3)=a^(3) meets the...

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  11. Show that the length of the portion of the tangent to the curve x^(2/3...

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  12. The sum of the intercepts made on the axes of coordinates by any tange...

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  13. Prove that the tangent at any point on the rectangular hyperbola xy = ...

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  14. Show that the segment of the tangent to the curve y=a/2I n((a+sqrt(a^2...

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  15. If alpha, beta are the intercepts made on the axes by the tangent at a...

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  16. Show that the segment of the tangent to the hyperbola y = frac{a^2}{x}...

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  17. Find the value of n in N such that the curve (x/a)^n+(y/b)^n=2 touche...

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  18. Find the equation of the normal to the curve y=(1+y)^y+sin^(-1)(sin^2x...

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  19. Prove that the equation of the normal to x^(2/3)+y^(2/3)=a^(2/3) is yc...

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  20. Find the equation of the normal to the curve x^2=4ywhich passes throu...

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  21. Find the points on the curve 9y^2=x^3 where normal to the curve makes ...

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