Home
Class 12
MATHS
The tangent at point P on the ellipse x^...

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 =`

A

`b^(2)`

B

`2b^(2)`

C

`a^(2)`

D

`2a^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|80 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 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 C is centre of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 and the normal at an end of a latusrectum cuts the major axis in G, then CG =

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

A tangent having slope of -4/3 to the ellipse (x^2)/(18)+(y^2)/(32)=1 intersects the major and minor axes at points A and B , respectively. If C is the center of the ellipse, then find area of triangle A B Cdot

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

S and T are the foci of the ellipse x^2/a^2+y^2/b^2 = 1 and B is an end of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is e then find value of 4e

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

A normal inclined at 45^@ to the axis of the ellipse x^2 /a^2 + y^2 / b^2 = 1 is drawn. It meets the x-axis & the y-axis in P & Q respectively. If C is the centre of the ellipse, show that the area of triangle CPQ is (a^2 - b^2)^2/(2(a^2 +b^2)) sq units

A point on the ellipse x^(2)/16 + y^(2)/9 = 1 at a distance equal to the mean of lengths of the semi - major and semi-minor axis from the centre, is

The tangents drawn from the point P to the ellipse 5x^(2) + 4y^(2) =20 are mutually perpendi­cular then P =

OBJECTIVE RD SHARMA ENGLISH-ELLIPSE-Chapter Test
  1. if vertices of an ellipse are (-4,1),(6,1) and x-2y=2 is focal chord t...

    Text Solution

    |

  2. If (-4, 3) and (8, 3) are the vertices of an ellipse whose eccentricit...

    Text Solution

    |

  3. If the chord joining points P(alpha) and Q(beta) on the ellipse ((x^...

    Text Solution

    |

  4. If P(alpha,beta) is a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1...

    Text Solution

    |

  5. The tangent at any point P on the ellipse meets the tangents at the ve...

    Text Solution

    |

  6. P is a point on the circle x^(2) + y^(2) = c^(2). The locus of the mid...

    Text Solution

    |

  7. The equation of the locus of the poles of normal chords of the ellipse...

    Text Solution

    |

  8. The locus of mid-points of focal chords of the ellipse (x^2)/(a^2)+(y^...

    Text Solution

    |

  9. The locus of a point whose polar with respect to the ellipse (x^2)/(a^...

    Text Solution

    |

  10. if the chord of contact of tangents from a point P to the hyperbola x...

    Text Solution

    |

  11. The locus of the poles of tangents to the auxiliary circle with respec...

    Text Solution

    |

  12. The locus of the poles of tangents to the director circle of the ellip...

    Text Solution

    |

  13. P is a point on the circle x^(2) + y^(2) = c^(2). The locus of the mid...

    Text Solution

    |

  14. If the tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 makes inte...

    Text Solution

    |

  15. If the tangents to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 make angles a...

    Text Solution

    |

  16. If C is centre of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 and the no...

    Text Solution

    |

  17. If the normals at P(theta) and Q(pi/2+theta) to the ellipse (x^2)/(a^2...

    Text Solution

    |

  18. about to only mathematics

    Text Solution

    |

  19. The tangent at point P on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 cu...

    Text Solution

    |

  20. If the lengths of major and semi-minor axes of an ellipse are 4 and sq...

    Text Solution

    |