Home
Class 12
MATHS
Two parabolas y^(2) = 4a(x – l(1)) and x...

Two parabolas `y^(2) = 4a(x – l_(1))` and `x^(2) = 4a(y – l_(2))` always touch one another, the quantities `l_(1)` and `l_(2)` are both variable. Locus of their point of contact has the equation

A

`xy=2a^2`

B

`xy=3a^2`

C

`xy=4a^2`

D

`xy=5a^2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise Numerical Value Type for JEE Main|15 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE MAIN ARCHIVE|15 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise LEVEL - 1|178 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos

Similar Questions

Explore conceptually related problems

Two parabolas y^(2)=4a(x-lamda_(1))andx^(2)=4a(y-lamda_(2)) always touch each other ( lamda_(1),lamda_(2) being variable parameters). Then their point of contact lies on a

Parabola y^2=4a(x-c_1) and x^2=4a(y-c_2) where c_1 and c_2 are variables, touch each other. Locus of their point of contact is

Let C : y =x^(2) -3, D : y = kx^(2) be two parabolas and L_(1) : x= a , L_(2) : x = 1 (a ne 0) be two straight lines. IF the line L_(1) meets the parabola C at a point B on the line L_(2) , other than A, then a may be equal to

Let the lines l_(1) and l_(2) be normals to y^(2)=4x and tangents to x^(2)=-12y (where l_(1) and l_(2) are not x - axis). The absolute value of the difference of slopes of l_(1) and l_(2) is

Two lines L_(1) and L_(2) of slops 1 are tangents to y^(2)=4x and x^(2)+2y^(2)=4 respectively, such that the distance d units between L_(1) and L _(2) is minimum, then the value of d is equal to

Consider three planes P_(1):x-y+z=1 , P_(2):x+y-z=-1 and P_(3):x-3y+3z=2 . Let L_(1),L_(2),L_(3) be the lines of intersection of the planes P_(2) and P_(3),P_(3) and P_(1),P_(1) and P_(2) respectively. Statement I Atleast two of the lines L_(1),L_(2) and L_(3) are non-parallel. Statement II The three planes do not have a common point.

Let P_(1) : y^(2) = 4ax and P_(2) : y^(2) =-4ax be two parabolas and L : y = x be a straight line. Equation of the tangent at the point on the parabola P_(1) where the line L meets the parabola is

Let P_(1) : y^(2) = 4ax and P_(2) : y^(2) =-4ax be two parabolas and L : y = x be a straight line. The co-ordinates of the other extremity of a focal chord of the parabola P_(2) one of whose extermity is the point of intersection of L and P_(2) is

Consider a plane x+y-z=1 and point A(1, 2, -3) . A line L has the equation x=1 + 3r, y =2 -r and z=3+4r . The equation of the plane containing line L and point A has the equation

Given equation of line L_(1) is y = 4 and line L2 is the bisector of angle O. Write the coordinates of point P.

VMC MODULES ENGLISH-CONIC SECTIONS-LEVEL - 2
  1. Chord of the parabola y^2+4y=(4)/(3)x-(16)/(3) which subtend right ang...

    Text Solution

    |

  2. about to only mathematics

    Text Solution

    |

  3. Two parabolas y^(2) = 4a(x – l(1)) and x^(2) = 4a(y – l(2)) always tou...

    Text Solution

    |

  4. If a sphere of mass m moving with velocity u collides with another ide...

    Text Solution

    |

  5. about to only mathematics

    Text Solution

    |

  6. The ordinates of points P and Q on the parabola y^2=12x are in the rat...

    Text Solution

    |

  7. Tangents at point B and C on the parabola y^2=4ax intersect at A. The ...

    Text Solution

    |

  8. The triangle formed by the tangent to the parabola y^2=4x at the point...

    Text Solution

    |

  9. The parabolas y=x^2-9" and "y=kx^2 intersect at points A and B. If len...

    Text Solution

    |

  10. If a chord which is normal to the parabola at one end subtend a right ...

    Text Solution

    |

  11. Set of values of 'h' for which the number of distinct common normals o...

    Text Solution

    |

  12. If the normal to the parabola y^2=4ax at the point (at^2, 2at)cuts the...

    Text Solution

    |

  13. On the parabola y^2 = 4ax, three points E, F, G are taken so that thei...

    Text Solution

    |

  14. PQ is a double ordinate of the parabola y^(2)=4ax. If the normal at P ...

    Text Solution

    |

  15. The equation of circle passing through co-normal points of y^2=4ax is:

    Text Solution

    |

  16. A tangent to the parabola y^2 + 4bx = 0 meets the parabola y^2 = 4ax i...

    Text Solution

    |

  17. A bag contains a total of 20 books on physics and mathematics, Any po...

    Text Solution

    |

  18. A tangent to the parabola y^2 + 4bx = 0 meets the parabola y^2 = 4ax i...

    Text Solution

    |

  19. Prove that the locus of the point of intersection of tangents to the p...

    Text Solution

    |

  20. P is parabola y^2=4ax and locus of mid points of all chords of this pa...

    Text Solution

    |