Home
Class 12
MATHS
Two parabola have the same focus. If the...

Two parabola have the same focus. If their directrices are the x-and the y-axis, respectively, then the slope of their common chord is

A

-1

B

`-1//2`

C

`-sqrt(3)//2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
(1) Let the focus be F. The parabola are open-down and open-right, respectively.
Let the parabolas intersect at point P and Q. From P, perpendiculars are drawn on the x-and the y-axis at A and B, respectively, Then,
PA=PF=PB
So, P lies on the line =-x.
Similarly, Q lies on the y=-x. Therefore, Slope of PQ =-1
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise EXERCISE (MULTIPLE CORRECT ANSWER TYPE )|26 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise LINKED COMPREHENSION TYPE|45 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.7|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

Two parabola have the same focus. If their directrices are the x-axis and the y-axis respectively, then the slope of their common chord is :

Let A and B be two distinct points on the parabola y^2=4x . If the axis of the parabola touches a circle of radius r having AB as its diameter, then find the slope of the line joining A and B .

The line x+ y +2=0 is a tangent to a parabola at point A, intersect the directrix at B and tangent at vertex at C respectively. The focus of parabola is S(a, 0) . Then

show that the equation of the parabola whose vertex and focus are on the x -axis at distances a and a' from the origin respectively is y^(2) = 4 (a'-a) (x - a )

The axis of parabola is along the line y=x and the distance of its vertex and focus from origin are sqrt2 and 2 sqrt2 respectively. If vertex and focus both lie in the first quadrant, then find the equation of the parabola

Let A, B be two distinct points on the parabola y^(2)=4x . If the axis of the parabola touches a circle of radius r having AB as diameter, the slope of the line AB is

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?

The distance of two points P and Q on the parabola y^(2) = 4ax from the focus S are 3 and 12 respectively. The distance of the point of intersection of the tangents at P and Q from the focus S is

If the coordinates of vertex and focus of a parabola be (2,1) & (2,3) respectively, then the axis of the parabola will be

The equation of the directrix of the parabola with vertex at the origin and having the axis along the x-axis and a common tangent of slope 2 with the circle x^2+y^2=5 is (are) x=10 (b) x=20 x=-10 (d) x=-20

CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
  1. A parabola y=a x^2+b x+c crosses the x-axis at (alpha,0)(beta,0) both ...

    Text Solution

    |

  2. The number of common chords of the parabolas x=y^2-6y+11 and y=x^2-6x+...

    Text Solution

    |

  3. Two parabola have the same focus. If their directrices are the x-and t...

    Text Solution

    |

  4. PSQ is a focal chord of a parabola whose focus is S and vertex is A. P...

    Text Solution

    |

  5. If P S Q is a focal chord of the parabola y^2=8x such that S P=6 , the...

    Text Solution

    |

  6. The triangle P Q R of area A is inscribed in the parabola y^2=4a x suc...

    Text Solution

    |

  7. If A1B1 and A2B2 are two focal chords of the parabola y^2=4a x , then ...

    Text Solution

    |

  8. If a and c are the lengths of segments of any focal chord of the parab...

    Text Solution

    |

  9. If y=m x+c touches the parabola y^2=4a(x+a), then (a)c=a/m (b) c=a m...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. The center of the circle which cuts parabola orthogonally the parabol...

    Text Solution

    |

  15. If the curve y=a x^2-6x+b pass through (0,2) and has its tangent paral...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. A tangent is drawn to the parabola y^2=4 x at the point P whose abscis...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |