Home
Class 11
MATHS
If the pair of straight lines x ysqrt(3)...

If the pair of straight lines `x ysqrt(3)-x^2=0` is tangent to the circle at `Pa n dQ` from the origin `O` such that the area of the smaller sector formed by `C Pa n dC Q` is `3pis qdotu n i t ,` where `C` is the center of the circle, the `O P` equals (a) `((3sqrt(3)))/2` (b) `3sqrt(3)` (c) 3 (d) `sqrt(3)`

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

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

If m(x-2)+sqrt(1-m^2) y= 3 , is tangent to a circle for all m in [-1, 1] then the radius of the circle is (a) 1.5 (b) 2 (c) 4.5 (d) 3

On the line segment joining (1, 0) and (3, 0) , an equilateral triangle is drawn having its vertex in the fourth quadrant. Then the radical center of the circles described on its sides. (a) (3,-1/(sqrt(3))) (b) (3,-sqrt(3)) (c) (2,-1/sqrt(3)) (d) (2,-sqrt(3))

If the line y-sqrt(3)x+3=0 cut the parabola y^2=x+2 at P and Q , then A PdotA Q is equal to [where A=(sqrt(3),0)] (a) (2(sqrt(3)+2))/3 (b) (4sqrt(3))/2 (c) (4(2-sqrt(2)))/3 (d) (4(sqrt(3)+2))/3

A curve is represented by the equations x=sec^2ta n dy=cott , where t is a parameter. If the tangent at the point P on the curve where t=pi/4 meets the curve again at the point Q , then |P Q| is equal to (5sqrt(3))/2 (b) (5sqrt(5))/2 (c) (2sqrt(5))/3 (d) (3sqrt(5))/2

The vertices of a triangle are (0,0), (x ,cosx), and (sin^3x ,0),w h e r e0ltxltpi/2 the maximum area for such a triangle in sq. units is (a) (3sqrt(3))/(32) (b) (sqrt(3)/32) (c) 4/32 (d) (6sqrt(3)) /(32)

In triangle A B C ,/_A=60^0,/_B=40^0,a n d/_C=80^0dot If P is the center of the circumcircle of triangle A B C with radius unity, then the radius of the circumcircle of triangle B P C is (a) 1 (b) sqrt(3) (c) 2 (d) sqrt(3) 2

A is a point on either of two lines y+sqrt(3)|x|=2 at a distance of 4/sqrt(3) units from their point of intersection. The coordinates of the foot of perpendicular from A on the bisector of the angle between them are (a) (-2/(sqrt(3)),2) (b) (0,0) (c) (2/(sqrt(3)),2) (d) (0,4)

If the area enclosed between the curves y=kx^2 and x=ky^2 , where kgt0 , is 1 square unit. Then k is: (a) 1/sqrt(3) (b) sqrt(3)/2 (c) 2/sqrt(3) (d) sqrt(3)

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Tangents P A and P B are drawn to x^2+y^2=9 from any arbitrary point P...

    Text Solution

    |

  2. The two circles which passes through (0,a) and (0,-a) and touch the li...

    Text Solution

    |

  3. If the pair of straight lines x ysqrt(3)-x^2=0 is tangent to the circl...

    Text Solution

    |

  4. The locus of the midpoint of a chord of the circle x^2+y^2=4 which sub...

    Text Solution

    |

  5. The condition that the chord xcos alpha +ysin alpha -p=0 of x^2+y^2-a^...

    Text Solution

    |

  6. Let the base A B of a triangle A B C be fixed and the vertex C lies on...

    Text Solution

    |

  7. If the chord of contact of tangents from a point P to a given circle p...

    Text Solution

    |

  8. Statement : Points (1, 1), (2, 3), and (3, 5) are collinear.

    Text Solution

    |

  9. Statement 1 : The number of circles touching lines x+y=1,2x-y=5, and 3...

    Text Solution

    |

  10. The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the...

    Text Solution

    |

  11. The equation of the chord of the circle x^2+y^2-3x-4y-4=0 , which pas...

    Text Solution

    |

  12. A rhombus is inscribed in the region common to the two circles x^2+y^2...

    Text Solution

    |

  13. In a triangle ABC, right angled at A, on the leg AC as diameter, semic...

    Text Solution

    |

  14. Two congruent circles with centered at (2, 3) and (5, 6) which inter...

    Text Solution

    |

  15. The locus of the center of the circle such that the point (2,3) is t...

    Text Solution

    |

  16. The value of 'c' for which the set {(x, y)|x^2+y^2+2xle1}bigcap{(x, y)...

    Text Solution

    |

  17. A circle of radius unity is centered at thet origin. Two particles tar...

    Text Solution

    |

  18. Two circles with radii a and b touch each other externally such that t...

    Text Solution

    |

  19. Consider: L1:2x+3y+p-3=0 L2:2x+3y+p+3=0 where p is a real number and...

    Text Solution

    |

  20. The straight line 2x - 3y = 1 divides the circular region x^2+y^2le6 i...

    Text Solution

    |