Home
Class 12
MATHS
An ellipse has eccentricity 1/2 and one...

An ellipse has eccentricity `1/2` and one focus at the point `P(1/2,1)`. Its one directrix is the comionand tangent nearer to the point the P to the hyperbolaof `x^2-y^2=1` and the circle `x^2+y^2=1`.Find the equation of the ellipse.

A

x=h,y=k

B

x=-h,y=-k

C

x=h,y=k

D

x=-k,y=-h

Text Solution

Verified by Experts

The correct Answer is:
b
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    MCGROW HILL PUBLICATION|Exercise QUESTION FROM PREVIOUS YEARS AIEEE/JEE MAIN PAPERS|23 Videos

  • HYPERBOLA

    MCGROW HILL PUBLICATION|Exercise QUESTION FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|8 Videos

  • HYPERBOLA

    MCGROW HILL PUBLICATION|Exercise EXERCISE LEVEL 1(SINGLE CORRECT ANSWER TYPE QUESTIONS)|25 Videos

  • HEIGHTS AND DISTANCES

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|3 Videos

  • INDEFINITE INTEGRATION

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B - ARCHITECTURE ENTRANCE EXAMINATION PAPERS|11 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the ellipse whose eccentricity is 1/2 , a focus is (2,3) and a directrix is x=7. Find the length of the major and minor axes of the ellipse .

Find the equation of the ellipse whose eccentricity is 1/2, the focus is (1,1) and the directrix is x-y+3=0

An ellipse has directrix x+y=-2 focus at (3,4) eccentricity =1//2, then length of latus rectum is

An ellipse , centred at the origin , has eccentricity 1/2 and one directrix d :x = 16 . If P : x = - 4 is a point on this ellipse , then SP =

The distance of a point on the ellipse (x^(2))/(6)+(y^(2))/(2)=1 from the centre is 2 Then the eccentric angle of the point is

5sqrt3x+7y=70 is a tangent to the ellipse x^2/49+y^2/25=1 at the point P. Find the coordinates of P and the equation of the normal at P .

Find the equation of the hyperbola whose : focus is (2,-1) directrix is 2x+3y=1 and eccentricity =2

Tangents are drawn from the point P(3,4) to the ellipse (x^(2))/(9)+(y^(2))/(4)=1 touching the ellipse at points A and B.

MCGROW HILL PUBLICATION-HYPERBOLA-EXERCISE LEVEL 2 (SINGLE CORRECT ANSWER TYPE QUESTIONS)
  1. Locus of the mid-point of the chord of the hyperbola which is a tange...

    Text Solution

    |

  2. H(1) xy = CA^(2) and H(2) : xy = k^(2) are two different hyper­bolas. ...

    Text Solution

    |

  3. e(1),e(2) are respectively the eccentricites of the hfyperbola x^(2)-...

    Text Solution

    |

  4. If theta is an angle between the two asymptotes of the hyperbola (x^(...

    Text Solution

    |

  5. A and B are two points on the hyperbola O is the centre. If OA is perp...

    Text Solution

    |

  6. The coordinates of a point common to a directrix and an asymptote of t...

    Text Solution

    |

  7. If the normals at P, Q, R on the rectangular hyperbola xy = c2 interse...

    Text Solution

    |

  8. If a diameter of a hyperbola meets the hyperbola in real points then

    Text Solution

    |

  9. An ellipse has eccentricity 1/2 and one focus at the point P(1/2,1)....

    Text Solution

    |

  10. Find the equation of the asymptotes of the hyperbola xy = hx + ky.

    Text Solution

    |

  11. A normal to the hyperbola (x^2)/4-(y^2)/1=1 has equal intercepts on th...

    Text Solution

    |

  12. A rectangular hyperbola of latus rectum 2 units pass­es through (0,0) ...

    Text Solution

    |

  13. Let H be a hyperbola of eccentricity 3. A normal to the hyperbola meet...

    Text Solution

    |

  14. Tangent at point P (a sec theta, b tan theta) to the hyperbola meets ...

    Text Solution

    |

  15. If two tangents drawn from the point (2, a) to the hyperbola are at ri...

    Text Solution

    |

  16. The locus of a point whose chord of contact with respect to the circle...

    Text Solution

    |

  17. If eccentricity of the hyperbola 4 and y = mx + c is a tangent to the...

    Text Solution

    |

  18. Asymptotes of a rectangular hyperbola are x = 5 and y = 4. If the hype...

    Text Solution

    |