Home
Class 11
MATHS
If the line l x+m y+n=0 cuts the elli...

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)` .

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Find the slope of normal to the ellipse , (x^(2))/(a^(2))+(y^(2))/(b^(2))=2 at the point (a,b).

If omega is one of the angles between the normals to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 (b>a) at the point whose eccentric angles are theta and pi/2+theta , then prove that (2cotomega)/(sin2theta)=(e^2)/(sqrt(1-e^2))

If e be the eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 , then e =

Find the maximum area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which touches the line y=3x+2.

A tangent is drawn to the ellipse to cut the ellipse x^2/a^2+y^2/b^2=1 and to cut the ellipse x^2/c^2+y^2/d^2=1 at the points P and Q. If the tangents are at right angles, then the value of (a^2/c^2)+(b^2/d^2) is

Find the coordinates of a point on the ellipse x^(2) + 2y^(2) = 4 whose eccentric angle is 60^(@)

If any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 intercepts equal lengths l on the axes, then find l .

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

Find the eccentric angles of the extremities of the latus recta of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1

Find the equation of the tangent to the ellipse x^2/a^2+y^2/b^2=1 at (x= 1,y= 1) .

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the number of rational points on the ellipse (x^2)/9+(y^2)/4=1.

    Text Solution

    |

  2. A line passing through the origin O(0,0) intersects two concentric ...

    Text Solution

    |

  3. If the line l x+m y+n=0 cuts the ellipse ((x^2)/(a^2))+((y^2)/(b^2)...

    Text Solution

    |

  4. Find the maximum area of an isosceles triangle inscribed in the ellips...

    Text Solution

    |

  5. Find the eccentric angles of the extremities of the latus recta of ...

    Text Solution

    |

  6. Find the equation of the ellipse whose axes are of length 6 and 2sq...

    Text Solution

    |

  7. If the equation (5x-1)^2+(5y-2)^2=(lambda^2-2lambda+1)(3x+4y-1)^2 repr...

    Text Solution

    |

  8. Obtain the equation of the ellipse whose focus is the point (-1, 1), a...

    Text Solution

    |

  9. The moon travels an elliptical path with Earth as one focus. The ma...

    Text Solution

    |

  10. If the foci of an ellipse are (0,+-1) and the minor axis of unit lengt...

    Text Solution

    |

  11. Let P be a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 of ecc...

    Text Solution

    |

  12. If C is the center of the ellipse 9x^2+16 y^2=144 and S is a focus,...

    Text Solution

    |

  13. Find the sum of the focal distances of any point on the ellipse 9x^...

    Text Solution

    |

  14. Find the lengths of the major and minor axis and the eccentricity of...

    Text Solution

    |

  15. Find the eccentricity, one of the foci, the directrix, and the leng...

    Text Solution

    |

  16. An ellipse passes through the point (4,-1) and touches the line x+4...

    Text Solution

    |

  17. If x/a+y/b=sqrt2 touches the ellipses x^2/a^2+y^2/b^2=1, then find the...

    Text Solution

    |

  18. Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the...

    Text Solution

    |

  19. An ellipse slides between two perpendicular straight lines. Then id...

    Text Solution

    |

  20. Find the locus of the foot of the perpendicular drawn from the cent...

    Text Solution

    |