Home
Class 12
MATHS
Prove that the curve (x/a)^n+(y/b)^n=2 t...

Prove that the curve `(x/a)^n+(y/b)^n=2` touches the straught line `x/a+y/b=2` at the point (a,b), whatever be the value of n.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

If x/a+y/b=2 touches the curve x^n/a^n+y^n/b^n=2 at the point (alpha,beta) then:

Show that the line (x)/(a)+(y)/(b)=1 touches the curve y= be ^(-(x)/(a)) at the point where it crosses the y-axis.

Show that the straight line (x)/(a)+(y)/(b)=2 touches the curve ((x)/(a))^(3)+((y)/(b))^(3)=2 , find the coordinates of the point of contact.

If the line x+y=6 is a normal to the parabola y^(2)=8x at point (a,b), then the value of a+b is ___________ .

If the equation of the tangent to the curve y^2=a x^3+b at point (2,3) is y=4x-5 , then find the values of a and b .

If the straight line lx+my+n=0 touches the : parabola y^(2)=4ax , prove that am^(2)=nl

For all values of n, the equation of the tangent to the curve ((x)/(a))^(n)+((y)/(b))^(n)=2 at the point (a,b) is (x)/(a)+(y)/(b)=k , find k.

If the line l x+m y+n=0 cuts the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 at points whose eccentric angles differ by pi/2, then find the value of (a^2l^2+b^2m^2)/(n^2) .

The line 3x+6y=k intersects the curve 2x^2+3y^2=1 at points A and B . The circle on A B as diameter passes through the origin. Then the value of k^2 is__________

If the parabola y=(a-b)x^2+(b-c)x+(c-a) touches x- axis then the line ax+by+c=0

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. Show that x=y^2 and xy = k cut orthogonally if 8k^2=1

    Text Solution

    |

  2. Show that curves ax^2+by^2=1 and cx^2+dy^2=1 intersect orthogonally if...

    Text Solution

    |

  3. Prove that the curve (x/a)^n+(y/b)^n=2 touches the straught line x/a+y...

    Text Solution

    |

  4. Prove that all points of the curve y^2=4a[x+asinx/a] at which the lang...

    Text Solution

    |

  5. Verify Rolle's theorem for f(x)=x^3(x-1)^2 in the interval 0lexle1

    Text Solution

    |

  6. If 2a+3b+6c=0 then the equation ax^2+bx+c=0 has in the interval (0,1)

    Text Solution

    |

  7. The value of 'c' of Rolls's throrem is applicable to the function f(x)...

    Text Solution

    |

  8. Find 'c' of the Lagrange's mean value theorem for the function f(x)=3x...

    Text Solution

    |

  9. If A(x1,y1) an B(x2,y2) be two points on the curve y=ax^2+bx+c then La...

    Text Solution

    |

  10. 0 < a < b < ( pi/2​) and f(a,b)= (tanb−tana)/b-a

    Text Solution

    |

  11. Let f,[2,7]rarr[0,oo) be a continuous and differentiable function, The...

    Text Solution

    |

  12. If y=1/(1+x^(n-m)+x^(p-m))+1/(1+x^(m-n)+x^(p-n))+1/(1+x^(m-p)+x^(n-p))...

    Text Solution

    |

  13. If y=|cosx|+|sinx|,then(dy/dx)"at"x=(2pi)/3 is

    Text Solution

    |

  14. The differential coefficient of f(logex) with respect to x, where f(x)...

    Text Solution

    |

  15. If f(x) = cosx. cos2x. Cos4x. Cos8x.cos16x, then f '(pi/4) is :

    Text Solution

    |

  16. If f(x)=log|2x|,x!=0 then f'(x) is equal to

    Text Solution

    |

  17. The derivative of an odd function is always

    Text Solution

    |

  18. If y=1/(1+x+x^2+x^3), then value of (d^2y)/(dx^2)at x=0 is

    Text Solution

    |

  19. The function f(x)=(cosx+isinx)(cos3x+isin3x)...{cos(2n-1)x+isin(2n-1)x...

    Text Solution

    |

  20. If y=sqrt(x+sqrt(y+sqrt(x+sqrty+...oo))) then (dy)/(dx) equal to

    Text Solution

    |