Home
Class 11
MATHS
The point of intersection of the tangent...

The point of intersection of the tangents at the point `P` on the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` and its corresponding point `Q` on the auxiliary circle meet on the line `x=a/e` (b) `x=0` `y=0` (d) none of these

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

The point of intersection of the tangents at the point P on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and its corresponding point Q on the auxiliary circle meet on the line (a) x=a/e (b) x=0 (c) y=0 (d) none of these

Show that the tangent at any point on an ellipse and the tangent at the corresponding point on its auxiliary circle intersect on the major axis.

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x0, y0).

The line y=2t^(2) intersects the ellipse (x^(2))/(9)+(y^(2))/(4)=1 in real points if

Find the point(s) of intersection of the line 2x + 3y = 18 and the circle x^2 + y^2 = 25

The ratio of the area of triangle inscribed in ellipse x^2/a^2+y^2/b^2=1 to that of triangle formed by the corresponding points on the auxiliary circle is 0.5. Then, find the eccentricity of the ellipse. (A) 1/2 (B) sqrt3/2 (C) 1/sqrt2 (D) 1/sqrt3

If alpha-beta= constant, then the locus of the point of intersection of tangents at P(acosalpha,bsinalpha) and Q(acosbeta,bsinbeta) to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is: (a) a circle (b) a straight line (c) an ellipse (d) a parabola

Find the lengths of the tangents drawn from the point. (x_(1),y_(1)) to the circle x^(2)+y^(2)+2x=0

The co-ordinate of a point on the auxiliary circle of the ellipse x^(2)+2y^(2)=4 corresponding to the point on the ellipse whose eccentric angle is 60^(@) will be

Find the point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Normal is drawn at one of the extremities of the latus rectum of the h...

    Text Solution

    |

  2. An ellipse and a hyperbola are confocal (have the same focus) and the ...

    Text Solution

    |

  3. The point of intersection of the tangents at the point P on the ellips...

    Text Solution

    |

  4. The distance between two directrices of a ractangular hyperbola is 10 ...

    Text Solution

    |

  5. Find the equation of normal to the hyperbola 3x^(2)-y^(2)=1 having slo...

    Text Solution

    |

  6. a triangle A B C with fixed base B C , the vertex A moves such that co...

    Text Solution

    |

  7. Find the equation of normal to the hyperbola x^(2)-9y^(2)=7 at point (...

    Text Solution

    |

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

    Text Solution

    |

  9. The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=...

    Text Solution

    |

  10. P N is the ordinate of any point P on the hyperbola (x^2)/(a^2)-(y^2)/...

    Text Solution

    |

  11. Show that the equation 9x^2-16 y^2-18 x+32 y-151=0 represents a hyperb...

    Text Solution

    |

  12. Find the equation of hyperbola, whose center is (-3,2), one vertex is ...

    Text Solution

    |

  13. An ellipse passing through the origin has its foci (3, 4) and (6, 8). ...

    Text Solution

    |

  14. The locus of the point of intersection of the lines sqrt3 x- y-4sqrt3 ...

    Text Solution

    |

  15. Find the eccentricity of the hyperbola with asymptotes 3x+4y=2 and 4x-...

    Text Solution

    |

  16. An ellipse having foci at (3, 3) and (-4,4) and passing through the or...

    Text Solution

    |

  17. If S and S'' are the foci, C is the centre, and P is a point on a rect...

    Text Solution

    |

  18. Pa n dQ are the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and B is...

    Text Solution

    |

  19. If P N is the perpendicular from a point on a rectangular hyperbola x ...

    Text Solution

    |

  20. A line of fixed length a+b moves so that its ends are always on two fi...

    Text Solution

    |