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`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

A circle of radius r passes through origin and cut the x-axis and y-axis at P and Q . The locus of foot of perpendicular drawn from origin upon line joining the points P and Q is (A) (x^2+y^2)^3=r^2(x^2y^2) (B) (x^2+y^2)^2(x+y)=r^2(xy) (C) (x^2+y^2)^2=r^2(x^2y^2) (D) (x^2+y^2)^3=4r^2(x^2y^2)

The locus of the foot of the perpendicular from the center of the hyperbola x y=1 on a variable tangent is (a) (x^2+y^2)^2=4x y (b) (x^2-y^2)=1/9 (x^2-y^2)=7/(144) (d) (x^2-y^2)=1/(16)

The locus of the foot of the perpendicular from the center of the hyperbola x y=1 on a variable tangent is (x^2+y^2)^2=4x y (b) (x^2-y^2)=1/9 (x^2-y^2)=7/(144) (d) (x^2-y^2)=1/(16)

The locus of the foot of the perpendicular from the center of the hyperbola x y=1 on a variable tangent is (a) (x^(2)+y^(2))^(2)=4xy (b) (x^2-y^2)=1/9 (c) (x^2-y^2)=7/(144) (d) (x^2-y^2)=1/(16)

The locus of the foot of perpendicular drawn from the centre of the ellipse x^2+""3y^2=""6 on any tangent to it is (1) (x^2-y^2)^2=""6x^2+""2y^2 (2) (x^2-y^2)^2=""6x^2-2y^2 (3) (x^2+y^2)^2=""6x^2+""2y^2 (4) (x^2+y^2)^2=""6x^2-2y^2

The locus of mid points of intercept made by tangents between co-ordinate axis of ellipse x^2+2y^2=2 is (A) 1/(4x^2)+1/(2y^2)=1 (B) x^2/2+y^2/4=1 (C) x^2/4+y^2/2=1 (D) 1/(2x^2)+1/(4y^2)=1

The locus of mid points of intercept made by tangents between co-ordinate axis of ellipse x^2+2y^2=2 is (A) 1/(4x^2)+1/(2y^2)=1 (B) x^2/2+y^2/4=1 (C) x^2/4+y^2/2=1 (D) 1/(2x^2)+1/(4y^2)=1

The equation of the curve passing through origin, whose slope at any point is (x(1+y))/(1+x^2) , is (A) (1+y)^2-x^2=1 (B) x^2+(y+1)^2=1 (C) (x+y)y=1-x^2 (D) x=ye^((1+y))

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

If tangents are drawn to the ellipse x^2+2y^2=2, then the locus of the midpoint of the intercept made by the tangents between the coordinate axes is (a) 1/(2x^2)+1/(4y^2)=1 (b) 1/(4x^2)+1/(2y^2)=1 (c) (x^2)/2+y^2=1 (d) (x^2)/4+(y^2)/2=1

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. A pair of tangents is drawn to a unit circle with center at the origin...

    Text Solution

    |

  2. A line meets the coordinate axes at 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 O and me...

    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=0 intersect ortho...

    Text Solution

    |

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

    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 ...

    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 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 origi...

    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

    |