Home
Class 12
MATHS
Parabola y^2=4a(x-c1) and x^2=4a(y-c2) w...

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

A

`xy=2a^(2)`

B

`xy=4a^(2)`

C

`xy=a^(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
(2) Let P(x,y) be the point of contact. At P, both of them must have the same slope. We have
`2y(dy)/(dx)=4a,2x=4a(dy)/(dx)`
Eliminating `dy//dx`, we get `xy=4a^(2)`.
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Exercise (Multiple)|26 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise (Comprehension)|41 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise 5.7|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Question Bank|19 Videos

Similar Questions

Explore conceptually related problems

Parabola y^(2)=4a(x-c_(1)) and x^(2)=4a(y-c_(2)), where c_(1) and c_(2) are variable,are such that they touch each other. The locus of their point of contact is xy=2a^(2) (b) xy=4a^(2)xy=a^(2)(d) none of these

Two parabolas y_(2) = 4a(x – 1l_(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

P(x,y) is a variable point on the parabola y^(2)=4ax and Q(x+c,y+c) is another variable point,where c is a constant.The locus of the midpoint of PQ is a/n parabola (b) hyperbola hyperbola (d) circle

y=x is tangent to the parabola y=ax^(2)+c . If c=2, then the point of contact is

y=x is tangent to the parabola y=ax^(2)+c . If c=2, then the point of contact is

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

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

A circle touches the parabola y^(2)=4x at (1,2) and also touches its directrix.The y- coordinates of the point of contact of the circle and the directrix is-

Let parabolas y=x(c-x) and y=x^(2)+ax+b touch each other at the point (1,0) then b-c=

CENGAGE-PARABOLA-Exercise (Single)
  1. If x=m x+c touches the parabola y^2=4a(x+a), then c=a/m (b) c=a m+a/...

    Text Solution

    |

  2. The area of the triangle formed by the tangent and the normal to the ...

    Text Solution

    |

  3. Parabola y^2=4a(x-c1) and x^2=4a(y-c2) where c1 and c2 are variables, ...

    Text Solution

    |

  4. Let y=f(x) be a parabola, having its axis parallel to the y-axis, whic...

    Text Solution

    |

  5. If y=2x-3 is tangent to the parabola y^2=4a(x-1/3), then a is equal to...

    Text Solution

    |

  6. The locus of the center of a circle which cuts orthogonally the parabo...

    Text Solution

    |

  7. If the parabola y=a x^2-6x+b passes through (0,2) and has its tangent ...

    Text Solution

    |

  8. Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at...

    Text Solution

    |

  9. The tangent to y^(2)=ax make angles theta(1)andtheta(2) with the x-axi...

    Text Solution

    |

  10. A tangent is drawn to the parabola y^2=4a x at the point P whose absci...

    Text Solution

    |

  11. The straight lines joining any point P on the parabola y^2=4a x to the...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. If the locus of the middle of point of contact of tangent drawn to the...

    Text Solution

    |

  15. If the bisector of angle A P B , where P Aa n dP B are the tangents to...

    Text Solution

    |

  16. From a point A(t) on the parabola y^(2)=4ax, a focal chord and a tange...

    Text Solution

    |

  17. The point of intersection of the tangents of the parabola y^(2)=4x dra...

    Text Solution

    |

  18. The angle between tangents to the parabola y^2=4ax at the points where...

    Text Solution

    |

  19. y=x+2 is any tangent to the parabola y^2=8xdot The point P on this tan...

    Text Solution

    |

  20. If y=m1x+c and y=m2x+c are two tangents to the parabola y^2+4a(x+a)=0 ...

    Text Solution

    |