Home
Class 12
MATHS
Show that curves ax^2+by^2=1 and cx^2+dy...

Show that curves `ax^2+by^2=1` and `cx^2+dy^2=1` intersect orthogonally if , `1/a-1/b=1/c-1/d`

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

The curves x^2/a+y^2/b=1 and x^2/a_1+y^2/b_1=1 will cut orthogonally if (a-b) =

If the curves ax^(2)+by^(2)=1 and cx^(2)+dy^(2)=1 intersect at right angles then show that (1)/(a)-(1)/(b)=(1)/(c)=(1)/(d)

The parabolas y^2=4ax and x^2=4by intersect orthogonally at point P(x_1,y_1) where x_1,y_1 != 0 provided (A) b=a^2 (B) b=a^3 (C) b^3=a^2 (D) none of these

If the curves (x^(2))/(a)+(y^(2))/(b)=1 and (x^(2))/(c )+(y^(2))/(d)=1 intersect at right angles then prove that a-b=c-d

Find the value of a if the curves (x^2)/(a^2)+(y^2)/4=1a n dy^3=16 x cut orthogonally.

ax^2+by^2=1" and "Ax^2+By^2=1 meet each other orthogonally. (aneA,bneB,aB-bA ne0) . Show that (1)/(a)-(1)/(b)=(1)/(A)-(1)/(B) .

Show that a^2(1+b^2)+b^2(1+c^2)+c^2(1+a^2)ge6abc .

The two curves x=y^2,x y=a^3 cut orthogonally at a point. Then a^2 is equal to 1/3 (b) 3 (c) 2 (d) 1/2

if b+c=a^2, c+a=b^2 and a+b=c^2 then find the value of 1/(1+a) + 1/(1+b) +1/(1+c)

Show that , A =1/3[[-1,2,-2],[-2,1,2],[2,2,1]] is proper orthogonal matrix .

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. Find the angle of intersection between the following curves, y^2=4x an...

    Text Solution

    |

  2. Show that x=y^2 and xy = k cut orthogonally if 8k^2=1

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. 0 < a < b < ( pi/2​) and f(a,b)= (tanb−tana)/b-a

    Text Solution

    |

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

    Text Solution

    |

  13. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. The derivative of an odd function is always

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |