Home
Class 11
MATHS
If ax^(2) + by^(2) = 1, a(1) x^(2) + b(1...

If `ax^(2) + by^(2) = 1, a_(1) x^(2) + b_(1)y^(2) = 1 ` , then show that the condition for orthogonality of above curves is `(1)/(a)-(1)/(b)=(1)/(a_(1))-(1)/(b_(1))`

Text Solution

Verified by Experts

The correct Answer is:
This is the required condition.
Promotional Banner

Topper's Solved these Questions

  • TANGENT AND NORMAL

    AAKASH SERIES|Exercise ADVANCED ANALYTICAL SOLVED EXAMPLES|5 Videos

  • TANGENT AND NORMAL

    AAKASH SERIES|Exercise EXERCISE 7.1 (SHORT ANSWER & LONG ANSWER QUESTIONS)|28 Videos

  • STRAIGHT LINES

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL-II (ADVANCED) PRACTICE SHEET (ADDVANCED)) (Comprehension Type Questions)|6 Videos

  • TRANSFORMATIONS

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I LEVEL-I Straight Objective Type Questions)|41 Videos

Similar Questions

Explore conceptually related problems

Find the condition for the orthogonality of the curves ax^2 + by^2 = 1 and a_1 x^2 + b_1 y^2 = 1

If one of the lines given by the equation a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)=0 coincides with one of the lines given by a_(2)x^(2)+2h_(2)xy+b_(2)y^(2)=0 and the other lines represented by them are perpendecular then prove that. h_(1)((1)/(a_(1))-(1)/(b_(1)))=h_(2)((1)/(a_(2))-(1)/(b_(2)))

If the pair of lines a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)=0 and a_(2)x^(2)+2h_(2)xy+b_(3)y^(2)=0 have one line in common then show that (a_(1)b_(2)-a_(2)b_(1))^(2)+4(a_(1)h_(2)-a_(2)h_(1))(b_(1)h_(2)-b_(2)h_(1))=0

Theorem : A necessary and sufficient condition for the quadratic equations a_(1)x^(2)+b_(1)x+c_(1)=0" and "a_(2)x^(2)+b_(2)x+c_(2)=0 to have a common roots is (c_(1)a_(2)-c_(2)a_(1))^(2)=(a_(1)b_(2)-a_(2)b_(1))(b_(1)c_(2)-b_(2)c_(1))

The Cartesian equation of the sides BC,CA, AB of a triangle are respectively u_(1)=a_(1)x+b_(1)y+c_(1)=0, u_(2)=a_(2)x+b_(2)y+c_(2)=0 and u_(3)=a_(3)x+b_(3)y+c_(3)=0 . Show that the equation of the straight line through A bisectig the side bar(BC) is (u_(3))/(a_(3)b_(1)-a_(1)b_(3))=(u_(2))/(a_(1)b_(2)-a_(2)b_(1))

If (a_(1), b_(1), c_(1)), (a_(2), b_(2), c_(2)) are d.r.'s of two perpendicular lines then

Find the equation of locus of point equidistant from the points (a_(1)b_(1)) and (a_(2),b_(2)) .

If (a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)) are direction ratio of two lines such that (a_(1)^(2)+b_(1)^(2)+c_(1)^(2))(a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2))^(2)=0 then the two lines

AAKASH SERIES-TANGENT AND NORMAL -ADVANCED SUBJECTIVE TYPE QUESTIONS
  1. If ax^(2) + by^(2) = 1, a(1) x^(2) + b(1)y^(2) = 1 , then show that ...

    Text Solution

    |

  2. Find the equations of tangent and normal to the curve ((x)/(a))^(4)+...

    Text Solution

    |

  3. Find the equations of tangent and normal to the curve ((x)/(a))^((2...

    Text Solution

    |

  4. Find the equations of tangent and normal to the curve y=(8)/(4+x^(2)...

    Text Solution

    |

  5. Find the equations of tangent and normal to the curve y=(6x)/(x^(2)-...

    Text Solution

    |

  6. Find the equations of tangent and normal to the curve 2x^(2)-xy+3y^(...

    Text Solution

    |

  7. Find the equations of tangent and normal to the curve (x^(2))/(a^(2)...

    Text Solution

    |

  8. Find the equations of tangent and normal to the curve (x^(2))/(a^(2)...

    Text Solution

    |

  9. Find the equations of tangent and normal to the curve x=a( theta- si...

    Text Solution

    |

  10. Find the equation of the tangent to the curve. 4x^(2)+9y^(2)=40 and ...

    Text Solution

    |

  11. Find the equation of the tangent to the curve. 9x^(2)+16y^(2)=52 and...

    Text Solution

    |

  12. Find the equation of the tangent to the curve. y=x^(3)+3x^(2)-5 and ...

    Text Solution

    |

  13. Find the points on the curve at which the tangents to the curve. y=x...

    Text Solution

    |

  14. Points at which the tangents to the hyperbola y=(x-1)/(x+1) are parlle...

    Text Solution

    |

  15. The point on the curve x^4-4x^3+4x^2+1 at which the tangent is paralle...

    Text Solution

    |

  16. The points on the curve 2a^2y=-x^3-3ax^2 at which the tangent is perpe...

    Text Solution

    |

  17. The points of contact of the tangents drawn from origin to the curve 3...

    Text Solution

    |

  18. Find the point of contact of the tangents drawn from origin to the cur...

    Text Solution

    |

  19. Tangent at any point of the curve ((x)/(a))^(2//3)+((y)/(b))^(2//3)=1 ...

    Text Solution

    |

  20. Show that the part of the tangent to the curve xy=a^(2) included betwe...

    Text Solution

    |

  21. The area of the triangle formed by the tangent and the normal at the p...

    Text Solution

    |