Home
Class 11
MATHS
Let E1a n dE2, respectively, be two elli...

Let `E_1a n dE_2,` respectively, be two ellipses `(x^2)/(a^2)+y^2=1,a n dx^2+(y^2)/(a^2)=1` (where `a` is a parameter). Then the locus of the points of intersection of the ellipses `E_1a n dE_2` is: (a) a set of curves comprising two straight lines (b) one straight line (c) one circle (d) one parabola

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 limiting position of the point of intersection of the straight lines 3x+5y=1 and (2+c)x+5c^2y=1 as c tends to one is:

If a tangent to the parabola y^2 = 4ax intersects the x^2/a^2+y^2/b^2= 1 at A and B , then the locus of the point of intersection of tangents at A and B to the ellipse is

The number of points of intersection of two curves y=2sinxa n dy=5x^2+2x+3i s a. 0 b. 1 c. 2 d. oo

Let the foci of the ellipse (x^(2))/(9) + y^(2) = 1 subtend a right angle at a point P . Then the locus of P is _

The locus of the point of intersection of two perpendicular tangents to the ellipse (x^(2))/(9) +(y^(2))/(4)=1 is -

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

If t is veriable paramete, parameter, show that the locus of the point of intersection of the straight lines (tx)/(a)+(y)/(b)-t = 0 and (x)/(a) - (ty)/(b) + 1 = 0 represents an ellipse

Two variable chords A Ba n dB C of a circle x^2+y^2=r^2 are such that A B=B C=r . Find the locus of the point of intersection of tangents at Aa n dCdot

Show that the line (ax)/(3)+(by)/(4)=c be a normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , When 15c=a^(2)e^(2) where e is the eccentricity of the ellipse.

A variable straight line through the point of intersection of the two lines (x)/(3)+(y)/(2)=1and(x)/(2)+(y)/(3)=1 meets the coordinate axes at A and B . Find the locus of the middle point of AB.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the equation of hyperbola : whose axes are coordinate axes and th...

    Text Solution

    |

  2. Find the equation of hyperbola if centre is (1, 0), one focus is (6, 0...

    Text Solution

    |

  3. Let E1a n dE2, respectively, be two ellipses (x^2)/(a^2)+y^2=1,a n dx^...

    Text Solution

    |

  4. Find the equation of hyperbola : Whose center is (3, 2), one focus is ...

    Text Solution

    |

  5. Consider the ellipse (x^2)/(f(k^2+2k+5))+(y^2)/(f(k+11))=1. If f(x) is...

    Text Solution

    |

  6. An ellipse and a hyperbola have their principal axes along the coordin...

    Text Solution

    |

  7. If hyperbola (x^(2))/(b^(2))-(y^(2))/(a^(2))=1 passes through the foci...

    Text Solution

    |

  8. If the tangent drawn at point (t^2,2t) on the parabola y^2=4x is the s...

    Text Solution

    |

  9. If the foci of the ellipse (x^2)/(16)+(y^2)/(b^2)=1 and the hyperbola ...

    Text Solution

    |

  10. Find the coordinates of the foci, the eccentricity, the latus rectum, ...

    Text Solution

    |

  11. If the latus rectum of a hyperbola forms an equilateral triangle with ...

    Text Solution

    |

  12. If the rectum subtends a right angle at the centre of the hyperbola (x...

    Text Solution

    |

  13. If PQ is a double ordinate of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b...

    Text Solution

    |

  14. Find the equation of the hyperbola given by equations x=(e^t+e^(-t))/2...

    Text Solution

    |

  15. A ray emerging from the point (5, 0) is incident on the hyperbola 9x^2...

    Text Solution

    |

  16. Normal is drawn at one of the extremities of the latus rectum of the h...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |