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

Parabola `y^2=4a(x-c_1)` and `x^2=4a(y-c_2)` , where `c_1a n dc_2` are variable, are such that they touch each other. The locus of their point of contact is (a)`x y=2a^2` (b) `x y=4a^2` (c)`x y=a^2` (d) none of these

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|4 Videos

Similar Questions

Explore conceptually related problems

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=3 (c) x+y=2 (d) none of these

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

A B C is a variable triangle such that A is (1,2) and B and C lie on line y=x+lambda (where lambda is a variable). Then the locus of the orthocentre of triangle A B C is (a) (x-1)^2+y^2=4 (b) x+y=3 (c) 2x-y=0 (d) none of these

Which one of the following curves cut the parabola at right angles? (a) x^2+y^2=a^2 (b) y=e^(-x//2a) (c) y=a x (d) x^2=4a y

If x=m x+c touches the parabola y^2=4a(x+a), then (a) c=a/m (b) c=a m+a/m (c) c=a+a/m (d) none of these

Two circle x^2+y^2=6 and x^2+y^2-6x+8=0 are given. Then the equation of the circle through their points of intersection and the point (1, 1) is (a) x^2+y^2-6x+4=0 (b) x^2+y^2-3x+1=0 (c) x^2+y^2-4y+2=0 (d)none of these

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

The parabolas y^2=4ac and x^2=4by intersect orthogonally at point P(x_1,y_1) where x_1,y_1 != 0 provided (A) b=a^2 (B) b=a^3 (C) b^3=a^2 (D) none of these

Let the parabolas y=x(c-x)a n dy=x^2+a x+b touch each other at the point (1,0). Then (a) a+b+c=0 (b) a+b=2 (c) b-c=1 (d) a+c=-2

The straight lines 4a x+3b y+c=0 , where a+b+c are concurrent at the point a) (4,3) b) (1/4,1/3) c) (1/2,1/3) d) none of these

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 c1a n dc2 are variable,...

    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=4 x at the point P whose abscis...

    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 the tangents to the parabola y^2=4a x at the points ...

    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

    |