Home
Class 12
MATHS
Find the condition for the line lx+my+...

Find the condition for the line
lx+my+n=0 to be a normal to the ellipse `x^2/a^2+y^2/b^2=1`

Text Solution

Verified by Experts

The correct Answer is:
`a^2/l^2+b^2/m^2=(a^2+b^2)^2/n^2` is the required condition.
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE4(A)|19 Videos
  • ELLIPSE

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE 4(B)|15 Videos
  • DIFFERENTIAL EQUATIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE- 8(e)|25 Videos
  • HYPERBOLA

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise SAQ|2 Videos

Similar Questions

Explore conceptually related problems

Find the condition for the line lx+my+n=0 to be a tangent to the ellipse x^2/a^2+y^2/b^2=1

The condition that the line lx + my + n= 0 to be a normal to the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2))= 1 is

The condition that the line lx +my+n =0 to be a normal to y^(2)=4ax is

Find the condition for the line Ix+my+ n = 0 is a normal to the circle x^2 + y^2 + 2gx + 2fy + c = 0 .

The condition that the line x/p+y/q=1 to be a tangent to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 is

Find the condition for the line x cos alpha +y sin alpha =p to be a tangent to the ellipse x^2/a^2+y^2/b^2=1 .

Find the condition for the straight line lx+my+n=0 to be a tangent to the parabola y^(2)=4ax and find the coordinates of the point of contact.

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-ELLIPSE-EXERCISE 4(B)
  1. Find the condition for the line lx+my+n=0 to be a normal to the ell...

    Text Solution

    |

  2. Find the equation of tangent and normal to the ellipse x^2+8y^2=33 at...

    Text Solution

    |

  3. Find the equation of tangent and normal to the ellipse x^2+2y^2-4x+1...

    Text Solution

    |

  4. Find the equation of the tangents to 9x^2+16y^2=144 , which makes equa...

    Text Solution

    |

  5. Find the co-ordinates for the points on the ellipse x^2+3y^2+37 at whi...

    Text Solution

    |

  6. Find the value of k if 4x+y+k=0 is a tangent to the ellipse x^2+3y^2=3...

    Text Solution

    |

  7. Find the condition for the line x cos alpha+y sin alpha=p to be a tang...

    Text Solution

    |

  8. Find the equations of tangent and normal to the ellipse 2x^2+3y^2=11 a...

    Text Solution

    |

  9. Find the equation to the tangents to the ellipse , x^2+2y^2+3 drawn fr...

    Text Solution

    |

  10. Find the equations of tangents to the ellipse 2x^2+y^2=8 which are P...

    Text Solution

    |

  11. Find the equations of tangents to the ellipse 2x^2+y^2=8 which are p...

    Text Solution

    |

  12. Find the equations of tangents to the ellipse 2x^2+y^2=8 which are w...

    Text Solution

    |

  13. A circle of radius 4, is concentric with the ellipse 3x^2+13y^2=78. Pr...

    Text Solution

    |

  14. Show that the foot of the perpendicular drawn from the centre on any t...

    Text Solution

    |

  15. Show that the locus of the feet of the perpendiculars drawn from foci ...

    Text Solution

    |

  16. The tangent and normal to the ellipse x^2+4y^2=4 at a point (theta) o...

    Text Solution

    |