Home
Class 11
MATHS
The normal at a variable point P on the ...

The normal at a variable point `P` on the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` of eccentricity `e` meets the axes of the ellipse at `Qa n dRdot` Then the locus of the midpoint of `Q R` is a conic with eccentricity `e '` such that (a)`e^(prime)` is independent of `e` (b) `e^(prime)=1` (c)`e^(prime)=e` (d) `e^(prime)=1/e`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

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

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

The normal at P to a hyperbola of eccentricity e , intersects its transverse and conjugate axes at L and M respectively. Show that the locus of the middle point of LM is a hyperbola of eccentricity e/sqrt(e^2-1)

Let S and S'' be the fociof the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentricity is i.e. P is a variable point on the ellipse. Consider the locus the incenter of DeltaPSS'' The eccentricity of the locus oc the P is (a) ellipse (b) hyperbola (a) parabola (d) circle

An ellipse has its centre C(1,3) focus at S( 6, 3) and passing through the point P(4, 7) then If the normal at a variable point on the ellipse meets its axes in Q and R then the locus of the mid-point of QR is a conic with an eccentricity (e') then

Find the area bounded by the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and the ordinates x = 0 and x = a e , where, b^2=a^2(1-e^2) and e < 1 .

If e_1 is the eccentricity of the ellipse x^2/16+y^2/25=1 and e_2 is the eccentricity of the hyperbola passing through the foci of the ellipse and e_1 e_2=1 , then equation of the hyperbola is

Let Sa n dS ' be two foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . If a circle described on S S^(prime) as diameter intersects the ellipse at real and distinct points, then the eccentricity e of the ellipse satisfies (a) e=1/(sqrt(2)) (b) e in (1/(sqrt(2)),1) (c) e in (0,1/(sqrt(2))) (d) none of these

The locus of the point ( (e^(t) +e^(-t))/( 2),(e^t-e^(-t))/(2)) is a hyperbola of eccentricity

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

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. The locus of the point of intersection of the tangent at the endpoints...

    Text Solution

    |

  2. A tangent drawn to hyperbola x^2/a^2-y^2/b^2 = 1 at P(pi/6) froms a t...

    Text Solution

    |

  3. The normal at a variable point P on the ellipse (x^2)/(a^2)+(y^2)/(b^2...

    Text Solution

    |

  4. If the distance between the foci and the distance between the two d...

    Text Solution

    |

  5. Any ordinate M P of the ellipse (x^2)/(25)+(y^2)/9=1 meets the auxilia...

    Text Solution

    |

  6. 1. If the distance between two parallel tangents drawn to the hyperbol...

    Text Solution

    |

  7. The number of distinct normal lines that can be drawn to the ellipse (...

    Text Solution

    |

  8. A normal is drawn to the hyperbolas (y-x m)(m y+x)=a^2 and (m^2-1)(y^2...

    Text Solution

    |

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

    Text Solution

    |

  10. The equation of the transvers axis of the hyperbola (x-3)^2+(y+1)^2=(4...

    Text Solution

    |

  11. Find the values of a for which three distinct chords drawn from (a ,0...

    Text Solution

    |

  12. If a variable line has its intercepts on the coordinate axes ea n de^(...

    Text Solution

    |

  13. Prove that if any tangent to the ellipse is cut by the tangents at the...

    Text Solution

    |

  14. A straight line has its extremities on two fixed straight lines and ...

    Text Solution

    |

  15. A circle has the same center as an ellipse and passes through the foci...

    Text Solution

    |

  16. The length of the transverse axis of the rectangular hyperbola x y=18 ...

    Text Solution

    |

  17. If P is any point on ellipse with foci S1 & S2 and eccentricity is 1/...

    Text Solution

    |

  18. The locus of the point which is such that the chord of contact of t...

    Text Solution

    |

  19. Find the range of eccentricity of the ellipse x^2/a^2+y^2/b^2=1, (wher...

    Text Solution

    |

  20. The angle between the lines joining origin to the points of intersect...

    Text Solution

    |