Home
Class 12
MATHS
If the normal at the point P( theta) ...

If the normal at the point `P( theta)` to the ellipse `(x^(2))/(14)/(y^(2))/(5)=1` intersects it again at the point Q `(2 , theta)` then ` cos theta` is equal to

A

`2//3`

B

`-2//3`

C

`3//2`

D

`-3//2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • THE ELLIPSE

    ML KHANNA|Exercise PROBLEM SET (2) (True and False)|4 Videos

  • THE ELLIPSE

    ML KHANNA|Exercise PROBLEM SET (2) (Fill in the blanks)|6 Videos

  • THE ELLIPSE

    ML KHANNA|Exercise PROBLEM SET (1) (Fill in the blanks)|4 Videos

  • THE CIRCLE

    ML KHANNA|Exercise Self Assessment Test (Fill in the blanks) |7 Videos

  • THE HYPERBOLA

    ML KHANNA|Exercise SELF ASSESSMENT TEST |4 Videos

Similar Questions

Explore conceptually related problems

Find the focal distance of point P(theta) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

The normal at a point P(theta) on the ellipse 5x^(2)+14y^(2)=70 cuts the curve again at a point Q(2 theta) then cos thetahat I

If the normal at theta on (x^(2))/(a^(2))+(y^(2))/(b^(2))=1,(a>b) intersects the curve again at phi then

If P(theta) and Q((pi)/(2)+theta) are two points on the ellipse (x^(2))/(9)+(y^(2))/(4)=1 then find the locus of midpoint of PQ

If P and Q are points with eccentric angles theta and (theta+(pi)/(6)) on the ellipse (x^(2))/(16)+(y^(2))/(4)=1 , then the area (in sq. units) of the triangle OPQ (where O is the origin) is equal to

If the focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, is normal at (a cos theta,b sin theta) then eccentricity of the ellipse is

If the length of the major axis intercepted between the tangent and normal at a point P (a cos theta, b sin theta) on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 is equal to the length of semi-major axis, then eccentricity of the ellipse is

If a tangent and a normal to the ellipse x^(2)+4y^(2)=4 at the point theta meets its major axis at P and Q such that PQ=2 then (1+cos theta)/(2)=

The points P,Q,R are taken on ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with eccentric angles theta,theta+a,theta+2a, then area of ,Delta PQR is independent of

The line 2x+y=3 cuts the ellipse 4x^(2)+y^(2)=5 at points P and Q. If theta is the acute angle between the normals at P and Q, then theta is equal to

ML KHANNA-THE ELLIPSE-PROBLEM SET (2) (Multiple Choice Questions)
  1. Find the equation of the normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)...

    Text Solution

    |

  2. The area of rectangle formed by perpendiculars from the centre of elli...

    Text Solution

    |

  3. If the normal at the point P( theta) to the ellipse (x^(2))/(14)...

    Text Solution

    |

  4. The locus of the mid-points of the portion of the tangents to the elli...

    Text Solution

    |

  5. Tangents are drawn to x^2 + 3y^2 = 2. The locus" of mid-point of inter...

    Text Solution

    |

  6. Tangents are drawn to ellipse (x^2)/(a^2) + (y^2)/(b^2) = 1 at points ...

    Text Solution

    |

  7. The locus of the point of intersection of tangents to an ellipse at tw...

    Text Solution

    |

  8. The eccentric angles of extremities of a chord of an ellipse (x^2)/(a^...

    Text Solution

    |

  9. The tangent at a point P(acosvarphi,bsinvarphi) of the ellipse (x^2)/(...

    Text Solution

    |

  10. If the line x+2y+4=0 cutting the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2...

    Text Solution

    |

  11. If P Q R is an equilateral triangle inscribed in the auxiliary circle ...

    Text Solution

    |

  12. On the ellipse 4x^(2)+9y^(2)=1, the points at which the tangent are pa...

    Text Solution

    |

  13. Tangents are drawn to the ellipse 3x^2 + 5y^2 = 32 and 25x^2 +9y^2 = 4...

    Text Solution

    |

  14. Let two perpendicular chords of the ellipse (x^2)/(a^2) + (y^2)/(b^2) ...

    Text Solution

    |

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

    Text Solution

    |

  16. Locus of mid-point of the focal chord of ellipse (x^(2))/(a^(2))+(y^(...

    Text Solution

    |

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

    Text Solution

    |

  18. If P(theta1) and D(theta2) be the end, points of two semi-conjugate di...

    Text Solution

    |

  19. If CP and CD are semi-conjugate diameters of the ellipse x^(2)/a^(2) +...

    Text Solution

    |

  20. CP and CD are conjugate semi-diameters of the ellipse x^(2)/a^(2) + y^...

    Text Solution

    |