Home
Class 12
MATHS
The number of common chords of the parab...

The number of common chords of the parabolas `x=y^2-6y+11` and `y=x^2-6x+11` is 1 (b) 2 (c) 4 (d) 6

A

1

B

2

C

4

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
(4) We have parabolas `x-2=(y-3)^(2)andy-2=(x-3)^(2)`
Parabolas are symmetrical about line y=x.

These parabola intersect at four points.
So, number of chords `=.^(4)C_(2)=6`
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 length of the common chord of the two circles x^2+y^2-4y=0 and x^2+y^2-8x-4y+11=0 is

Axis of the parabola x^2 - 3y - 6x + 6 = 0 is

The number of common tangents to the circles x^(2) + y^(2) = 4 and x^(2)+y^(2)-6x-8y=24 is

Find the length of the common chord of the circles x^2+y^2+2x+6y=0 and x^2+y^2-4x-2y-6=0

Which of the following is a point on the common chord of the circle x^2+y^2+2x-3y+6=0 and x^2+y^2+x-8y-31=0? (a) (1,-2) (b) (1,4) (c)(1,2) (d) 1,-4)

Find the length of the common chord of the parabola y^2=4(x+3) and the circle x^2+y^2+4x=0 .

If the length of the common chord of two circles x^2+y^2+8x+1=0 and x^2+y^2+2muy-1=0 is 2sqrt(6) , then the values of mu are (a) +-2 (b) +-3 (c) +-4 (d) none of these

If the focus of the parabola x^2-k y+3=0 is (0,2), then a values of k is (are) 4 (b) 6 (c) 3 (d) 2

The coordinates of the ends of a focal chord of the parabola y^2=4a x are (x_1, y_1) and (x_2, y_2) . Then find the value of x_1x_2+y_1y_2 .

If P S Q is a focal chord of the parabola y^2=8x such that S P=6 , then the length of S Q is (a)6 (b) 4 (c) 3 (d) none of these

CENGAGE-PARABOLA-Exercise (Single)
  1. If P is a point on the parabola y^2=3(2x-3) and M is the foot perpendi...

    Text Solution

    |

  2. A parabola y=a x^2+b x+c crosses the x-axis at (alpha,0) and (beta,0) ...

    Text Solution

    |

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

    Text Solution

    |

  4. Two parabolas have the same focus. If their directrices are the x- and...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. If aa n dc are the lengths of segments of any focal chord of the parab...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. Parabola y^2=4a(x-c1) and x^2=4a(y-c2) , where c1a n dc2 are variable,...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |