Home
Class 12
MATHS
The circles x^2 + y^2 + 2g1x- a^2=0 and ...

The circles `x^2 + y^2 + 2g_1x- a^2=0 and x^2 + y^2 + 2g_2x-a^2 = 0` cut each other orthogonally. If `p_1 and p_2` are perpendicular from `(0,a) and (0,-a)` on a common tangent of these circles , then` p_1p_2` is equal to

A

`a ^(2) //2`

B

`a ^(2)`

C

`2a ^(2)`

D

`a ^(2) + 2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • CIRCLES AND SYSTEMS OF CIRCLES

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (NUMERICAL ANSWER TYPE QUESTIONS )|17 Videos
  • CIRCLES AND SYSTEMS OF CIRCLES

    MCGROW HILL PUBLICATION|Exercise EXERCISE (CONCEPT-BASED ( SINGLE CORRECT ANSWER TYPE QUESTIONS ))|20 Videos
  • CIRCLES AND SYSTEMS OF CIRCLES

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (LEVEL 1 ( SINGLE CORRECT ANSWER TYPE QUESTIONS ))|55 Videos
  • CARTESIAN SYSTEM OF RECTANGULAR COORDINATES AND STRAIGHT LINES

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B - ARCHITECTURE (ENTRANCE EXAMINATION PAPERS)|14 Videos
  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPER|17 Videos

Similar Questions

Explore conceptually related problems

The circles x^(2)+y^(2)+2g_(1)x-a^(2)=0 and x^(2)+y^(2)+2g_(2)x-a^(2)=0 cut each other orthogonally.If p_(1) and p_(2) are perpendicular from (0,a) and (0,-a) on a common tangent of these circles,then p_(1)p_(2) is equal to

Show that the circles x^2 + y^2 - 2x-6y-12=0 and x^2 + y^2 + 6x+4y-6=0 cut each other orthogonally.

If circles x^(2) + y^(2) + 2gx + 2fy + c = 0 and x^(2) + y^(2) + 2x + 2y + 1 = 0 are orthogonal , then 2g + 2f - c =

If circles x^(2) + y^(2) + 2gx + 2fy + e = 0 and x^(2) + y^(2) + 2x + 2y + 1 = 0 are orthogonal , then 2g + 2f - e =

If two circle x^(2)+y^(2)+2gx +2fy=0 and x^(2)+y^(2)+2g'x+2f'y=0 touch each other then f'g =fg'.

The circles ax^2+ay^2+2g_1 x +2f_1 y+c_1 = 0 and bx_2+by^2+2g_2x+2f_2y+c_2=0 a ne 0 and b ne 0 0cut orthogonally if

MCGROW HILL PUBLICATION-CIRCLES AND SYSTEMS OF CIRCLES -SOLVED EXAMPLES (LEVEL 2 ( SINGLE CORRECT ANSWER TYPE QUESTIONS ))
  1. Let A0A1A2A3A4A5 be a regular hexagon inscribed in a circle of unit ra...

    Text Solution

    |

  2. For each natural number k. Let C(k) denotes the circle with radius k c...

    Text Solution

    |

  3. C1 and C2 are circle of unit radius with centers at (0, 0) and (1, 0),...

    Text Solution

    |

  4. A chord of the circle x^2 + y^2 - 4x - 6y = 0 passing through the orig...

    Text Solution

    |

  5. On the line joining the points A (0,4) and B (3,0), a square ABCD is c...

    Text Solution

    |

  6. A circle with center at the origin and radius equal to a meets the axi...

    Text Solution

    |

  7. Equation of a circle having radius equal to twice the radius of the ci...

    Text Solution

    |

  8. A circle C1 of radius b touches the circle x^2 + y^2 =a^2 externally a...

    Text Solution

    |

  9. Two circles, each of radius 5 units, touch each other at (1, 2). If th...

    Text Solution

    |

  10. The locus of points of intersection of the tangents to x^(2)+y^(2)=a^...

    Text Solution

    |

  11. If theta is the angle subtended by the circle S -= x ^(2) + y ^(2) + 2...

    Text Solution

    |

  12. If the area of the quadrilateral formed by the tangent from the origin...

    Text Solution

    |

  13. An equation chord joining the points (1,2) and (2,-1) subtends an angl...

    Text Solution

    |

  14. An equation of a common tangent to the circle x ^(2) + y ^(2) + 14 x -...

    Text Solution

    |

  15. The locus of the point, the sum of the squares of whose distances from...

    Text Solution

    |

  16. An isosceles triangle ABC is inscribed in a circle x^2+y^2=a^2 with t...

    Text Solution

    |

  17. If the chord of contact of the tangents drawn from a point on the c...

    Text Solution

    |

  18. If the line 3x - 4y - k = 0 (k gt 0) touches the circle x^(2)+y^(2)-4x...

    Text Solution

    |

  19. The circles x^2 + y^2 + 2g1x- a^2=0 and x^2 + y^2 + 2g2x-a^2 = 0 cut e...

    Text Solution

    |

  20. A circle C touches the x-axis and the circle x ^(2) + (y-1) ^(2) =1 ex...

    Text Solution

    |