Home
Class 12
MATHS
If the normal at any point P on ellipse ...

If the normal at any point P on ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2)) =1` meets the auxiliary circle at Q and R such that `/_QOR = 90^(@)` where O is centre of ellipse, then

A

`a^(4) + 2b^(4) ge 3a^(2)b^(2)`

B

`a^(4) + 2b^(4) ge 5a^(2)b^(2) + 2a^(3)b`

C

`a^(4) + 2b^(4) ge 3a^(2)b^(2) + ab`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|7 Videos

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • EXPONENTIAL AND LOGARITHMIC SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|20 Videos

Similar Questions

Explore conceptually related problems

If normal at any point P to ellipse (x^2)/(a^2) + (y^2)/(b^2) = 1(a > b) meet the x & y axes at A and B respectively. Such that (PA)/(PB) = 3/4 , then eccentricity of the ellipse is:

If normal at any poin P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (agtbgt0) meets the major and minor axes at Q and R, respectively, so that 3PQ=2PR, then find the eccentricity of ellipse

If the normal at any point P of the ellipse (x^(2))/(16)+(y^(2))/(9) =1 meets the coordinate axes at M and N respectively, then |PM|: |PN| equals

P and Q are two points on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 whose eccentric angles are differ by 90^(@) , then

The tangent at point P on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 cuts the minor axis in Q and PR is drawn perpendicular to the minor axis. If C is the centre of the ellipse, then CQ*CR =

P and Q are corresponding points on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 and the auxiliary circle respectively . The normal at P to the elliopse meets CQ at R. where C is the centre of the ellipse Prove that CR = a +b

If the normal at any point P of the ellipse x^2/a^2 + y^2/b^2 = 1 meets the major and minor axes at G and E respectively, and if CF is perpendicular upon this normal from the centre C of the ellipse, show that PF.PG=b^2 and PF.PE=a^2 .

If the normal at point P (theta) on the ellipse x^2/a^2 + y^2/b^2 = 1 meets the axes of x and y at M and N respectively, show that PM : PN = b^2 : a^2 .

The tangent and normal at any point P of an ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 cut its major axis in point Q and R respectively. If QR=a prove that the eccentric angle of the point P is given by e^(2)cos^(2)phi+cosphi-1=0

The line x = at^(2) meets the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 in the real points iff

OBJECTIVE RD SHARMA ENGLISH-ELLIPSE-Exercise
  1. If C is the centre of the ellipse 9x^(2) + 16y^(2) = 144 and S is one ...

    Text Solution

    |

  2. In an ellipse the distance between the foci is 8 and the distance betw...

    Text Solution

    |

  3. The centre of the ellipse 4x^(2) + 9y^(2) + 16x - 18y - 11 = 0 is

    Text Solution

    |

  4. If P is any point on the ellipse 9x^(2) + 36y^(2) = 324 whose foci are...

    Text Solution

    |

  5. An ellipse is described by using an ellipse string which is passed ove...

    Text Solution

    |

  6. Two perpendicular tangents drawn to the ellipse (x^2)/(25)+(y^2)/(16)=...

    Text Solution

    |

  7. The distance of the point 'theta' on the ellipse x^(2)/a^(2) + y^(2)/b...

    Text Solution

    |

  8. If y = mx + c is a tangent to the ellipse x^(2) + 2y^(2) = 6, them c^(...

    Text Solution

    |

  9. Let P be a variable point on the ellipse x^(2)/25 + y^(2)/16 = 1 with ...

    Text Solution

    |

  10. The ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and the straight line y=mx+c int...

    Text Solution

    |

  11. Let E be the ellipse (x^2)/9+(y^2)/4=1 and C be the circle x^2+y^2=9 ....

    Text Solution

    |

  12. Equation of the ellipse with accentricity 1/2 and foci at (pm 1, 0), i...

    Text Solution

    |

  13. If B and B' are the ends of minor axis and S and S' are the foci of th...

    Text Solution

    |

  14. The length of the axes of the conic 9x^(2)+4y^(2)-6x+4y+1=0 ,are

    Text Solution

    |

  15. If the normal at any point P on ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)...

    Text Solution

    |

  16. If the curves x^(2) + 4y^(2) = 4, x^(2) + a^(2) y^(2) = a^(2) for suit...

    Text Solution

    |

  17. If P(theta),Q(theta+pi/2) are two points on the ellipse x^2/a^2+y^2/b^...

    Text Solution

    |

  18. An ellipse has point (1,-1)a n d(2,-1) as its foci and x+y-5=0 as one ...

    Text Solution

    |

  19. If the length of the semi major axis of an ellipse is 68 and the eccen...

    Text Solution

    |

  20. If the tangent at the point (4 cos theta, (16)/(sqrt(11)) sin theta) t...

    Text Solution

    |