Home
Class 12
MATHS
If the circles x^2 + y^2 + 2ax + cy + a ...

If the circles `x^2 + y^2 + 2ax + cy + a =0` and `x^2 + y^2 - 3ax + dy - 1 = 0` intersect in two distinct points P and Q then the line 5x + by - a = 0 passes through P and Q for

A

exactly one value of a

B

no value of a

C

infinitely many values of a

D

exactly two values of a

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • SYSTEM OF CIRLES

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SET -1)|9 Videos
  • SYSTEM OF CIRLES

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SET -2)|1 Videos
  • SYSTEM OF CIRLES

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SET-4 )|4 Videos
  • STRAIGHT LINES

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS) (SET-4)|12 Videos
  • THE PLANE

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS) SET 4|4 Videos

Similar Questions

Explore conceptually related problems

If the circles x^2+y^2+2ax+cy+a=0 and x^2+y^2-3ax+dy-1=0 intersect in two distinct points P and Q then show that the line 5x+6y-a=0 passes through P and Q for no value of a.

If the two circles (x - 1)^(2) + (y - 3)^(2) = r^(2) and x^(2) + y^(2) - 8x+ 2y + 8 = 0 intersect at two distinct points, then

If the two circles (x-2)^(2)+(y-3)^(2)=r^(2) and x^(2)+y^(2)-10x+2y+17=0 intersect in two distinct point then

If the two circles (x-1)^(2)+(y-3)^(2)=r^(2) and x^(2)+y^(2)-8x+2y+8=0 intersect in two distinct points, then

If the circles (x-1)^(2)+(y-3)^(2)=4r^(2) and x^(2)+y^(2)-8x+2y+8=0 intersect in two distinct points, then show that 1ltrlt 4 .

If P and Q are the Points of intersection of the circles x^2 + y^2 + 3x + 7y -2p - 5 = 0 and x^2 +y^2 +2x +2y- p^2 =0 then there is a circle passing through P, Q and (1, 1) for

The circles x^(2)+y^(2)=4x+8y+5 intersects the line 3x-4y = m at two distinct points of

DIPTI PUBLICATION ( AP EAMET)-SYSTEM OF CIRLES -EXERCISE 1
  1. A line l meets the circle x^(2) + y^(2) = 61 in A , B and P(-5,6) i...

    Text Solution

    |

  2. The circles x^(2) + y^(2) = 1 , x^(2) + y^(2) + 6x - 2y = 1 " and " ...

    Text Solution

    |

  3. If the circles x^2 + y^2 + 2ax + cy + a =0 and x^2 + y^2 - 3ax + dy - ...

    Text Solution

    |

  4. If aa circle passes through the point (a,b) and cuts the cirlce x^(2)...

    Text Solution

    |

  5. The locus of the centre of the circle, which cuts the circle x^(2) + y...

    Text Solution

    |

  6. A circle passes through the points (3,4) and cuts the circle x^(2) + ...

    Text Solution

    |

  7. The equation of the common tangent at the point contact of the circles...

    Text Solution

    |

  8. The equation of the common chord of the two circles x^(2) +y^(2) + 2...

    Text Solution

    |

  9. The equation of the common chord of the two circles (x -a)^(2) + (y...

    Text Solution

    |

  10. The distance from (1,2) to the radical axis of the circles x^(2) + ...

    Text Solution

    |

  11. The distanc of the point (1,-2) from the common chord of the circles ...

    Text Solution

    |

  12. The distance of the point (1,-2) from the common chord of the circles ...

    Text Solution

    |

  13. The length of the common chord of the circles of radii 15 and 20, whos...

    Text Solution

    |

  14. The length of the common chord of the circles x^(2) + y^(2) + 2x + ...

    Text Solution

    |

  15. The length of the common chord of the two circles x^(2) + y^(2) - 4y ...

    Text Solution

    |

  16. The length of the common chord of the circles x^(2) + y^(2) + 2hx = 0...

    Text Solution

    |

  17. The equation of the common chord of the two circles (x -a)^(2) + (y...

    Text Solution

    |

  18. The length of the common chord of the circles (x - a)^(2) + (y - b)...

    Text Solution

    |

  19. The length of the common chord of the circles x^(2) + y^(2) + 2gx ...

    Text Solution

    |

  20. The length of the common chord of the circle x^(2) + y^(2) + ax + b...

    Text Solution

    |