Home
Class 12
MATHS
The axis of parabola is along the line y...

The axis of parabola is along the line y=x and the distance of its vertex and focus from origin are `sqrt2` and 2`sqrt2` respectively. If vertex and focus both lie in the first quadrant, then the equation of the parabola is :

A

`(x+y)^2=(x-y-2)`

B

`(x-y)^2=(x+y+2)`

C

`(x-y)^2=4(x+y-2)`

D

`(x-y)^2=8(x+y-2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|15 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|28 Videos

Similar Questions

Explore conceptually related problems

The axis of parabola is along the line y=x and the distance of its vertex and focus from origin are sqrt(2) and 2sqrt(2) respectively.If vertex and focus both lie in the first quadrant,then the equation of the parabola is:

The axis of a parabola is along the line y=x and the distance of its vertex and focus from the origin are sqrt(2) and 2sqrt(2), respectively.If vertex and focus both lie in the first quadrant, then the equation of the parabola is (x+y)^(2)=(x-y-2)(x-y)^(2)=4(x+y-2)(x-y)^(2)=4(x+y-2)(x-y)^(2)=4(x+y-2)(x-y)^(2)=8(x+y-2)

The axis of a parabola is along the line y = x and the distance of its vertex from origin is sqrt2 and that from its focus is 2sqrt2 . If vertex and focus both lie in the first quadrant, then the equation of the parabola is

The axis of a parabola is along the line y = x and its vertex and focus are in the first quadrant at distances sqrt2,2sqrt2 respectively, from the origin. The equation of the parabola, is

If the points (0,4) and (0,2) are respectively the vertex and focus of a parabola,then find the equation of the parabola.

A parabola has its vertex and focus in the first quadrant and axis along the line y=x . If the distances of the vertex and focus from the origin are respectively sqrt(2)&2sqrt(2) , then equation of the parabola is x^2+y^2-8x+8y+2x y=16 x^2+y^2-8x-8y+16=2x y (x-y)^2=8(x+y-2) (x+y)^2=(x-y+2)

If (0, 3) and (0, 2) are respectively the vertex and focus of a parabola, then its equation, is

ARIHANT MATHS-PARABOLA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Tangent to the curve y=x^2+6 at a point (1,7) touches the circle x^2+y...

    Text Solution

    |

  2. let P be the point (1, 0) and Q be a point on the locus y^2= 8x. The l...

    Text Solution

    |

  3. The axis of parabola is along the line y=x and the distance of its ver...

    Text Solution

    |

  4. The equations of the common tangents to the parabola y = x^2 and y=-...

    Text Solution

    |

  5. The locus of the vertices of the family of parabolas y =[a^3x^2]/3 + [...

    Text Solution

    |

  6. Angle between the tangents to the curve y=x^2-5x+6 at the points (2,0)...

    Text Solution

    |

  7. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  8. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  9. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  10. Statement I The curve y = x^2/2+x+1 is symmetric with respect to the l...

    Text Solution

    |

  11. The equation of a tangent to the parabola y^2=""8x""i s""y""=""x""+...

    Text Solution

    |

  12. Consider the two curves C1 ; y^2 = 4x, C2 : x^2 + y^2 - 6x + 1 = 0 the...

    Text Solution

    |

  13. A parabola has the origin as its focus and the line x=2 as the directr...

    Text Solution

    |

  14. The tangent PT and the normal PN to the parabola y^2=4ax at a point P...

    Text Solution

    |

  15. Let A and B be two distinct points on the parabola y^2 = 4x. If the ax...

    Text Solution

    |

  16. If two tangents drawn from a point P to the parabola y2 = 4x are at ri...

    Text Solution

    |

  17. Consider the parabola y^2 = 8x. Let Delta1 be the area of the triangle...

    Text Solution

    |

  18. Let (x,y) be any point on the parabola y^2 = 4x. Let P be the point t...

    Text Solution

    |

  19. Let (x,y) be any point on the parabola y^2 = 4x. Let P be the point t...

    Text Solution

    |

  20. The shortest distance between line y-x=1 and curve x=y^2 is

    Text Solution

    |