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

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos
  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 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 .

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. The angle of intersection between the curves y=[|sinx|+|cosx|]andx^2+y...

    Text Solution

    |

  2. Find the value of a in order that f(x)=sqrt(3)sinx-cosx-2a x+b decreas...

    Text Solution

    |

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

    Text Solution

    |

  4. Discuss the monotonocity of function f(x)=2log|x-1|-x^2+2x+3.

    Text Solution

    |

  5. If the area of the triangle included between the axes and any tangent ...

    Text Solution

    |

  6. Separate the intervals of monotonocity for the function f(x)=3cos^4x+1...

    Text Solution

    |

  7. If the tangent at (x1,y1) to the curve x^3+y^3=a^3 meets the curve aga...

    Text Solution

    |

  8. Separate the intervals of monotonocity for the function f(x)=3cos^4x+1...

    Text Solution

    |

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

    Text Solution

    |

  10. Separate the intervals of monotonocity for the function f(x)=((log)e x...

    Text Solution

    |

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

    Text Solution

    |

  12. Discuss monotonocity of f(x)=x/(sinx)a n d g(x)=x/(tanx),where (xlt=1...

    Text Solution

    |

  13. Prove that the curves y=f(x),[f(x)>0],a n dy=f(x)sinx ,w h e r ef(x) i...

    Text Solution

    |

  14. Discuss the extremum of f(x)={x^2+x^-2}

    Text Solution

    |

  15. Tangents are drawn from the origin to curve y=sinxdot Prove that point...

    Text Solution

    |

  16. Write the maximum value of f(x)=x^(1//x) .

    Text Solution

    |

  17. Given f(x)=4-(1/2-x)^(2/3),g(x)={("tan"[x])/x ,x!=0 1,x=0 , h...

    Text Solution

    |

  18. Determine the local maxima and local minima of f(x)=x^3-6x^2+12x-8 is

    Text Solution

    |

  19. Show that the angle between the tangent at any point P and the line jo...

    Text Solution

    |

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

    Text Solution

    |