Home
Class 12
MATHS
If x cos alpha + y sin alpha = p is a ta...

If `x cos alpha + y sin alpha = p` is a tangent to the curve
`(x/a)^(n/n-1) +(y/b)^(n/n-1) = 1`then so that
`(a cos alpha)^n + (b sin alpha)^n = p^n`.

Promotional Banner

Topper's Solved these Questions

  • AREA UNDER PLANE CURVES

    MODERN PUBLICATION|Exercise PROBLEM|2 Videos

Similar Questions

Explore conceptually related problems

If the straight line x cos alpha + y sin alpha = p touches the curve (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 , then prove that a^(2) cos^(2) alpha + b^(2) sin^(2) alpha = p^(2) .

Find the condition that the line x cos alpha+y sin alpha = P mam be a tangent to the curve x^2/a^2+y^2/b^2=1 .

Differentiate tan^(-1) ((x sin alpha)/(1-x cos alpha))

What is the inverse of A = ((cos alpha,sin alpha),(sin alpha,-cos alpha))

If "sin"^(-1)(x/a) + "sin"^(-1) (y/b)=alpha "prove that" x^2/a^2+(2xy)/(ab) "cos" alpha+y^2/b^2 ="sin"^2 alpha

If y=e^x+e^-x+2 has a tangent parallel to x-axis at (alpha,beta) then find the value of alpha .

If tanbeta=(n^2sinalpha cdot cosalpha)/(1-n^2sin^2alpha) then show that tan(alpha-beta)/(tanalpha)=1-n^2

If A_alpha = [(cos alpha, sin alpha),(-sin alpha, cos alpha)] , then what is the value of A_alphaA_beta .

MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-PROBLEM
  1. Show that the function e^x/x^p is strictly increasing for x gt p gt 0.

    Text Solution

    |

  2. Show that x/(1+ x tan x,) x in (0,pi/2)is maximum when x = cos x.

    Text Solution

    |

  3. Find the extreme values of y = cos x(1+sin x), x in [0,2pi]

    Text Solution

    |

  4. Find the equation of normal to the curve x^3 =4y which passes through ...

    Text Solution

    |

  5. Prove that y=mx+c touches the parabola y^2 = 4ax if a=mc.

    Text Solution

    |

  6. If f(x) = a In x + bx^2 + x has extreme values at x= - 1 and x = 2 the...

    Text Solution

    |

  7. Find the intervals where the following functions are (a) increasing an...

    Text Solution

    |

  8. Find extreme value of f(x).={{:((x)/(1-x^2),-1ltxlt0),(x^3-x,0lexlt2):...

    Text Solution

    |

  9. Find the values of x for which f(x) = x^4+2x^3-2x^2-6x+5 is locally ma...

    Text Solution

    |

  10. Show that the tangent to the curve y=x^2+3x-2 at (1,2) is parallel to ...

    Text Solution

    |

  11. Find the altitude of a right circular cylinder of maximum volume inscr...

    Text Solution

    |

  12. Show that y=mx+c is a tangent to the ellipse x^2/a^2+y^2/b^2=1 if c^2=...

    Text Solution

    |

  13. A square piece of tin of side 18 cm is to be made into a box without t...

    Text Solution

    |

  14. Show that the equation of the normal to x^(2/3) + y^(2/3) = a^(2/3)is ...

    Text Solution

    |

  15. Find the interval where y=sin2x-cos2x,xin[0,2pi] is (a) incresing (b)...

    Text Solution

    |

  16. A cylindrical vessel of capacity 500 cubic metres open at the top is t...

    Text Solution

    |

  17. Find the points on the curve y = x^2+1 which are nearest to the point ...

    Text Solution

    |

  18. Find the condition that the line x cos alpha+y sin alpha = P mam be a ...

    Text Solution

    |

  19. Show that the semi-vertical angle of a right circular cone of minimum ...

    Text Solution

    |

  20. If x cos alpha + y sin alpha = p is a tangent to the curve (x/a)^(n/...

    Text Solution

    |