Home
Class 11
MATHS
A circle of constant radius a passes thr...

A circle of constant radius `a` passes through the origin `O` and cuts the axes of coordinates at points `P` and `Q` . Then the equation of the locus of the foot of perpendicular from `O` to `P Q` is
(A) `(x^2+y^2)(1/(x^2)+1/(y^2))=4a^2`
(B)`(x^2+y^2)^2(1/(x^2)+1/(y^2))=a^2`
(C) `(x^2+y^2)^2(1/(x^2)+1/(y^2))=4a^2`
(D) `(x^2+y^2)(1/(x^2)+1/(y^2))=a^2`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

A circle of radius r passes through the origin and intersects the x-axis and y-axis at P and Q respectively. Show that the equation to the locus of the foot of the perpendicular drawn form the origin upon the line segment bar (PQ) is (x^(2)+y^(2))^(3)=4r^(2)x^(2)y^(2) .

The line x =2 y intersects the ellipse (x^(2))/(4) +y^(2) = 1 at the points P and Q . The equation of the circle with pq as diameter is _

The locus of the foot of the perpendicular from the origin on each member of the family (4a+ 3)x - (a+ 1)y -(2a+1)=0 (a) (2x-1)^(2) +4 (y+1)^(2) = 5 (b) (2x-1)^(2) +(y+1)^(2) = 5 (c) (2x+1)^(2)+4(y-1)^(2) = 5 (d) (2x-1)^(2) +4(y-1)^(2) = 5

A straight line through the origin 'O' meets the parallel lines 4x +2y= 9 and 2x +y=-6 at points P and Q respectively. Then the point 'O' divides the segment PQ in the ratio : (A) 1:2 (B) 3:2 (C) 2:1 D) 4:3

A triangle is formed by the lines x+y=0,x-y=0, and l x+m y=1. If la n dm vary subject to the condition l^2+m^2=1, then the locus of its circumcenter is (a) (x^2-y^2)^2=x^2+y^2 (b) (x^2+y^2)^2=(x^2-y^2) (c) (x^2+y^2)^2=4x^2y^2 (d) (x^2-y^2)^2=(x^2+y^2)^2

A circle S passes through the point (0, 1) and is orthogonal to the circles (x - 1)^2 +y^2=16 and x^2+y^2=1 . Then

The slope of the tangent at (x , y) to a curve passing through a point (2,1) is (x^2+y^2)/(2x y) , then the equation of the curve is

The equation of the circle whose diameter is the common chord of the circles x^2+y^2+3x+2y+1=0 and x^2+y^2+3x+4y+2=0 is

If points A and B are (1, 0) and (0, 1), respectively, and point C is on the circle x^2+y^2=1 , then the locus of the orthocentre of triangle A B C is (a) x^2+y^2=4 (b) x^2+y^2-x-y=0 (c) x^2+y^2-2x-2y+1=0 (d) x^2+y^2+2x-2y+1=0

A circle s passes through the point ( 0,1) and is orthogonal to the circles ( x - 1)^(2) + y^(2) = 16 and x^(2) + y^(2) = 1 . Then

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. A pair of tangents are drawn to a unit circle with centre at the origi...

    Text Solution

    |

  2. A line meets the co-ordinate axes in A and B. A circle is circumscribe...

    Text Solution

    |

  3. A circle of constant radius a passes through the origin O and cuts the...

    Text Solution

    |

  4. The equation of the line inclined at an angle of pi/4 to the x-axis ,s...

    Text Solution

    |

  5. If a circle of constant radius 3K passes through the origin and meets ...

    Text Solution

    |

  6. A straight line l1 with equation x-2y+10=0 meets the circle with equat...

    Text Solution

    |

  7. Let C be a circle with two diameters intersecting at an angle of 30^0d...

    Text Solution

    |

  8. If the circles x^2 + y^2 + 2x + 2ky + 6 = 0 and x^2 + y^2 + 2ky + k = ...

    Text Solution

    |

  9. The triangle PQR is inscribed in the circle x^2+y^2=25. If Q and R hav...

    Text Solution

    |

  10. A circle is given by x^2 + (y-1) ^2 = 1, another circle C touches it e...

    Text Solution

    |

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

    Text Solution

    |

  12. The centre of circle inscribed in a square formed by lines x^2-8x+12...

    Text Solution

    |

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

    Text Solution

    |

  14. Consider square A B C D of side length 1. Let P be the set of all segm...

    Text Solution

    |

  15. The number of intergral value of y for which the chord of the circle x...

    Text Solution

    |

  16. Statement 1 : The circle having equation x^2+y^2-2x+6y+5=0 intersects ...

    Text Solution

    |

  17. Statement 1 : The center of the circle having x+y=3 and x-y=1 as its n...

    Text Solution

    |

  18. Statement 1 : The equations of the straight lines joining the origin...

    Text Solution

    |

  19. Statement 1 : Points A(1,0),B(2,3),C(5,3),a n dD(6,0) are concyclic. S...

    Text Solution

    |

  20. Statement I The chord of contact of tangent from three points A, B and...

    Text Solution

    |