Home
Class 12
MATHS
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`

Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise CHECK YOUR UNDERSTANDING|10 Videos

  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise COMPLETITION FILE (Questions from JEE Main)|18 Videos

  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise Exercise|15 Videos

  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

Similar Questions

Explore conceptually related problems

if the straight line x cos alpha+y sin alpha=p touches the curve x^(m)y^(n)=a^(m+n) prove that p^(m+n)m^(m)n^(n)=(m+n)^(m+n)a^(m+n)sin^(n)alpha cos^(m)alpha

If m cos alpha-n sin alpha=p then prove that m sin alpha+n cos alpha=+-sqrt(m^(2)+n^(2)-p^(2))

If in an HP, t_m=n and t_n=m then prove that t_(m+n)=(mn)/(m+n) .

If (tan theta + sin theta) =m and (tan theta - sin theta) = n , prove that (m^(2)-n^(2))^(2)=16mn.

lim_(x rarr a)(x^(m)-a^(m))/(x^(n)-a^(n))=((m)/(n))a^(m-n) if m>n

If tan theta+sin theta=m and tan theta-sin theta=n then prove m^(2)-n^(2)=4sqrt(mn)

If a^m .a^n = a^(mn) , then m(n - 2) + n(m- 2) is :

If cos theta-sin theta=m and cos theta+sin theta=n then prove that (m^2-n^2)/(m^2+n^2)=-2sin theta cos theta

MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-Revision Exercise
  1. Show that the line d/a+y/b=1 touches the curve y=b e^(-x/a) at the poi...

    Text Solution

    |

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

    Text Solution

    |

  3. if the straight line xcosalpha+y sin alpha=p touches the curve x^my^n=...

    Text Solution

    |

  4. Find the point on the curve y=3x^2-9x+8 at which the tangents are equa...

    Text Solution

    |

  5. The equation of the tangent at (2,3) on the curve y^2=a x^3+b is y=4x-...

    Text Solution

    |

  6. A circular disc of radius 3 cm is being heated. Due to expansion, i...

    Text Solution

    |

  7. The radius of a sphere shrinks from 10 to 9.8 cm. Find approximatel...

    Text Solution

    |

  8. If the error committed in measuring the radius of a circle is 0.01%, f...

    Text Solution

    |

  9. If a triangle ABC, inscribed in a fixed circle, be slightly varied in ...

    Text Solution

    |

  10. The area S of a triangle is calculated by measuring the sides b and c,...

    Text Solution

    |

  11. The pressure p and the volume v of a gas are connected by the relat...

    Text Solution

    |

  12. Show that the function given by f(x)=(logx)/xhas maximum at x = e.

    Text Solution

    |

  13. The sum of the perimeter of a circle and square is k, where k is so...

    Text Solution

    |

  14. Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 h...

    Text Solution

    |

  15. Show that s in^p\ theta\ cos^q\ theta attains a maximum, when theta...

    Text Solution

    |

  16. The fraction exceeds its p^(th) power by the greatest number possible...

    Text Solution

    |

  17. If the sum of the lengths of the hypotenues and a side of a right a...

    Text Solution

    |

  18. Divide 4 into two positive numbers such that the sum of the square of ...

    Text Solution

    |

  19. A cylindrical can to be made to hold 1 litres of oil. Find the dimensi...

    Text Solution

    |

  20. Find the shortest distance of the point (0, c) from the curve y=x^(2),...

    Text Solution

    |