Home
Class 12
MATHS
If the line x cos alpha + y sin alpha = ...

If the line `x cos alpha + y sin alpha = p` represents the common chod APQB of the circle `x ^(2) + y ^(2) =a ^(2) and x ^(2) + y ^(2) =b ^(2) (a gt b)` as shown in the then AP is equal to

A

`sqrt (a ^(2) +p^(2)) + sqrt (b ^(2) + p^(2))`

B

`sqrt (a ^(2) -p^(2)) + sqrt (b ^(2) - p^(2))`

C

`sqrt(a ^(2) + p^(2)) - sqrt ( b ^(2) - p^(2))`

D

`sqrt(a ^(2) + p^(2)) - sqrt (b ^(2) + p^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CIRCLES AND SYSTEMS OF CIRCLES

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (LEVEL 2 ( SINGLE CORRECT ANSWER TYPE QUESTIONS ))|30 Videos

  • 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 SOLVED EXAMPLES (CONCEPT - BASED ( SINGLE CORRECT ANSWER TYPE QUESTIONS ))|20 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

If the equation x cos theta + y sin theta = p represents the equation of common chord APQB of the circles x^(2) +y^(2) =a^(2) and x^(2) +y^(2) =b^(2)(a gt b ) then AP is equal to :

If the line y cos alpha = x sin alpha +a cos alpha be a tangent to the circle x^(2)+y^(2)=a^(2) , then

If line x cos alpha + y sin alpha = p " touches circle " x^(2) + y^(2) =2ax then p =

The line x cos alpha+y sin alpha=p will be a tangent to the circle x^(2)+y^(2)-2ax cos alpha-2ay sin alpha=0.1fp=

The line x cos alpha + y sin alpha +y sin alpha =p is tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1. if

The line x sin alpha - y cos alpha =a touches the circle x ^(2) +y ^(2) =a ^(2), then,

Show that the straight line x cos alpha+y sin alpha=p touches the curve xy=a^(2), if p^(2)=4a^(2)cos alpha sin alpha

MCGROW HILL PUBLICATION-CIRCLES AND SYSTEMS OF CIRCLES -SOLVED EXAMPLES (LEVEL 1 ( SINGLE CORRECT ANSWER TYPE QUESTIONS ))
  1. The circles x ^(2) + y ^(2) -10 x + 16=0 and x ^(2) + y ^(2) =r ^(2) i...

    Text Solution

    |

  2. A line is drawn through the point P(3,11) to cut the circle x^(2)+y^(2...

    Text Solution

    |

  3. If the line x cos alpha + y sin alpha = p represents the common chod A...

    Text Solution

    |

  4. A circle touches both the coordinate axes and the line x-y=sqrt(2)a, a...

    Text Solution

    |

  5. If the tangent at the point on the circle x^2+y^2+6x +6y=2 meets the ...

    Text Solution

    |

  6. An acute triangle PQR is inscribed in the circle x^2+y^2= 25. If Q and...

    Text Solution

    |

  7. Two vertices of an equilateral triangle are (-1,0) and (1, 0), and its...

    Text Solution

    |

  8. An isosceles triangle is inscribed in the circle x ^(2) + y ^(2) - 6x ...

    Text Solution

    |

  9. Find the equations to the common tangents of the circles x^2+y^2-2x-6y...

    Text Solution

    |

  10. The centre of the circle whose radius is 5 and which touches the circl...

    Text Solution

    |

  11. A point moves such that the sum of the squares of its distances from t...

    Text Solution

    |

  12. Equation of a circle with centre (-4,3) touching internally and contai...

    Text Solution

    |

  13. The equations of the tangents drawn from the origin to the circle x^2 ...

    Text Solution

    |

  14. A square is inscribed in the circle x^2+y^2-2x+4y-93=0 with its sides ...

    Text Solution

    |

  15. An equation of a circle touching the axes of coordinates and the line ...

    Text Solution

    |

  16. If one of the diameters of the circle x^2+y^2-2x-6y+ 6 = 0 is a chord ...

    Text Solution

    |

  17. The centres of a set of circles, each of radius 3, lie on the circle x...

    Text Solution

    |

  18. If a circle passes through the point (a,b) and cuts the circle x^(2)+y...

    Text Solution

    |

  19. Consider a family of circles which are passing through the point (-...

    Text Solution

    |

  20. If the circles x^2+y^2+2a x+c y+a=0 and points Pa n dQ , then find the...

    Text Solution

    |