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 ENGLISH|Exercise EXERCISE (MULTIPLE CORRECT ANSWER TYPE )|26 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise LINKED COMPREHENSION TYPE|45 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise Concept Applications Exercise 5.7|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE ENGLISH|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE ENGLISH|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

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

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

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 (a) parabola (b) hyperbola (c) circle (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 a/n parabola (b) hyperbola hyperbola (d) circle

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

Tangent are drawn from two points (x_1, y_1) and (x_2, y_2) to xy = c^2 . The conic passing through the two points and through the four points of contact will be circle if (A) x_1 x_2 = y_1 y_2 (B) x_1 y_2 = x_2 y_1 (C) x_1 y_2 + x_2 y_1 = 4c^2 (D) x_1 x_1 + y_1 y_2 = 4c^2

If the line x + y = 1 touches the parabola y^2-y + x = 0 , then the coordinates of the point of contact are:

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

The curve xy = c(c > 0) and the circle x^2 +y^2=1 touch at two points, then distance between the points of contact is

Consider two curves C1:y^2=4x ; C2=x^2+y^2-6x+1=0 . Then, a. C1 and C2 touch each other at one point b. C1 and C2 touch each other exactly at two point c. C1 and C2 intersect(but do not touch) at exactly two point d. C1 and C2 neither intersect nor touch each other

CENGAGE ENGLISH-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
  1. If y=m x+c touches the parabola y^2=4a(x+a), then (a)c=a/m (b) c=a m...

    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. find the equation of hyperabola where foci are (0,12) and (0,-12)and t...

    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 drawn...

    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+c)=0 ...

    Text Solution

    |