Home
Class 12
MATHS
The shortest distance between the parabo...

The shortest distance between the parabolas `2y^2=2x-1` and `2x^2=2y-1` is `2sqrt(2)` (b) `1/2sqrt(2)` (c) 4 (d) `sqrt((36)/5)`

A

`1/(2sqrt2)`

B

`1/2`

C

`2sqrt2`

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|14 Videos
  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|24 Videos
  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|25 Videos
  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos
  • PERMUTATIONS AND COMBINATIONS

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

Similar Questions

Explore conceptually related problems

The shortest distance between the parabolas 2y^2=2x-1 and 2x^2=2y-1 is: (a) 2sqrt(2) (b) 1/(2sqrt(2)) (c) 4 (d) sqrt((36)/5)

Equation of normal to parabola y^2 = 4ax at (at^2, 2at) is y-2at = -t(x-at^2) i.e. y=-tx+2at + at^3 Greatest and least distances between two curves occur along their common normals. Least and greatest distances of a point from a curve occur along the normal to the curve passing through that point. Shortest distance between parabola 2y^2-2x+1=0 and 2x^2-2y+1=0 is: (A) 1/2 (B) 1/sqrt(2) (C) 1/(2sqrt(2)) (D) 2sqrt(2)

The shortest distance between line y-x=1 and curve x=y^2 is (a) (3sqrt2)/8 (b) 8/(3sqrt2) (c) 4/sqrt3 (d) sqrt3/4

The shortest distance between the parabola y^2 = 4x and the circle x^2 + y^2 + 6x - 12y + 20 = 0 is : (A) 0 (B) 1 (C) 4sqrt(2) -5 (D) 4sqrt(2) + 5

The distance between the parallel lnes y=2x+4 and 6x-3y-5 is (A) 1 (B) 17/sqrt(3) (C) 7sqrt(5)/15 (D) 3sqrt(5)/15

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

The minimum vertical distance between the graphs of y=2+sinx and y=cosx is (a) 2 (b) 1 (c) sqrt(2) (d) 2-sqrt(2)

The shortest distance between line y"-"x""=""1 and curve x""=""y^2 is : (1) (sqrt(3))/4 (2) (3sqrt(2))/8 (3) 8/(3sqrt(2)) (4) 4/(sqrt(3))

The area bounded between the parabolas x^2=y/4"and"x^2=9y and the straight line y""=""2 is (1) 20sqrt(2) (2) (10sqrt(2))/3 (3) (20sqrt(2))/3 (4) 10sqrt(2)

If P(1+t/(sqrt(2)),2+t/sqrt(2)) is any point on a line, then the range of the values of t for which the point P lies between the parallel lines x+2y=1a n d2x+4y=15. is (a) (4sqrt(2))/3lttlt5(sqrt(2)) 6 (b) 0lttlt(5sqrt(2)) (c) 4sqrt(2)lttlt0 (d) none of these

ARIHANT MATHS ENGLISH-PARABOLA-Exercise (Single Option Correct Type Questions)
  1. If the normals to the parabola y^2=4a x at P meets the curve again at ...

    Text Solution

    |

  2. The normal to the parabola y^(2)=4ax at three points P,Q and R meet at...

    Text Solution

    |

  3. about to only mathematics

    Text Solution

    |

  4. The largest value of a for which the circle x^2+y^2=a^2 falls totally ...

    Text Solution

    |

  5. From a point (sintheta,costheta), if three normals can be drawn to the...

    Text Solution

    |

  6. If two different tangents of y^2=4x are the normals to x^2=4b y , then...

    Text Solution

    |

  7. The shortest distance between the parabolas 2y^2=2x-1 and 2x^2=2y-1 is...

    Text Solution

    |

  8. Normals at two points (x1y1)a n d(x2, y2) of the parabola y^2=4x meet ...

    Text Solution

    |

  9. A line is drawn form A(-2,0) to intersect the curve y^2=4x at Pa n dQ ...

    Text Solution

    |

  10. An equilateral triangle SAB is inscribed in the parabola y^(2)=4ax hav...

    Text Solution

    |

  11. C is the center of the circle with center (0, 1) and radius unity. P i...

    Text Solution

    |

  12. Let S be the focus of y^2=4x and a point P be moving on the curve such...

    Text Solution

    |

  13. If P be a point on the parabola y^2=3(2x-3) and M is the foot of perpe...

    Text Solution

    |

  14. Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixe...

    Text Solution

    |

  15. Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q...

    Text Solution

    |

  16. A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to...

    Text Solution

    |

  17. If the fourth term in the expansion of (a x+1/x)i s5/2,\ then find th...

    Text Solution

    |

  18. The set of points on the axis of the parabola y^2-4x-2y+5=0 find the s...

    Text Solution

    |

  19. The tangent to the parabola y=x^2 has been drawn so that the abscissa ...

    Text Solution

    |

  20. if y=4x+3 is parallel to a tangent to the parabola y^2=12x, then its d...

    Text Solution

    |