Home
Class 12
MATHS
A rectangular hyperbola whose centre is ...

A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. Then, `CP^2 +CQ^2 +CR^2 + CS^2 =` (A) `r^2` (B) `2r^2` (C) `3r^2` (D) `4r^2`

A

`r^(2)`

B

`2r^(2)`

C

`3r^(2)`

D

`4r^(2)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION -I ( Subjective Type Questions )|24 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise section-J (Aakash Challengers Qestions)|13 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise section - J|6 Videos

Similar Questions

Explore conceptually related problems

If P + Q = R and P - Q = S, prove that R^2 + S^2 = 2(P^2 + Q^2)

P, Q, and R are the feet of the normals drawn to a parabola ( y−3 ) ^2 =8( x−2 ) . A circle cuts the above parabola at points P, Q, R, and S . Then this circle always passes through the point. (a) ( 2, 3 ) (b) ( 3, 2 ) (c) ( 0, 3 ) (d) ( 2, 0 )

A circle of radius r cm has a diameter of length (a) r cm (b) 2r cm (c) 4r cm (d) r/2c m

If the sum of the areas of two circles with radii r_1 and r_2 is equal to the area of a circle of radius r , then r_1^2 +r_2^2 (a) > r^2 (b) =r^2 (c)

Consider the points P(2,-4);Q(4,-2) and R(7,1). The points P,Q,R

Tangent is drawn at any point (p ,q) on the parabola y^2=4a x .Tangents are drawn from any point on this tangant to the circle x^2+y^2=a^2 , such that the chords of contact pass through a fixed point (r , s) . Then p ,q ,r and s can hold the relation (A) r^2q=4p^2s (B) r q^2=4p s^2 (C) r q^2=-4p s^2 (D) r^2q=-4p^2s

AB and AC are two chords of a circle of radius r such that AB=2AC. If p and q are the distances of AB and AC from the centre Prove that 4q^(2)=p^(2)+3r^(2) .

The area of a sector whose perimeter is four times its radius r units, is (a) (r^2)/4 sq. units (b) 2r^2 sq. units (c) r^2 sq. units (d) (r^2)/2 sq. units

A solid sphere of radius r is melted and cast into the shape of a solid cone of height r , the radius of the base of the cone is (a) 2r (b) 3r (c) r (d) 4r

In P Q R ,\ \ Q M_|_P R and P R^2-P Q^2=Q R^2 . Prove that Q M^2=P MxxM R

AAKASH INSTITUTE ENGLISH-CONIC SECTIONS-SECTION - J ( Aakash Challengers Questions )
  1. Find the angle between the two tangents from the origin to the circle ...

    Text Solution

    |

  2. The area of the triangle formed by the tangent at (3, 4) to the circle...

    Text Solution

    |

  3. If P(1), P(2), P(3) are the perimeters of the three circles, S(1) :...

    Text Solution

    |

  4. If (1, a), (b, 2) are conjugate points with repect to the circle x^(2)...

    Text Solution

    |

  5. Area of the equilateral triangle inscribed in the circle x^(2) + y^(2)...

    Text Solution

    |

  6. A solid sphere of radius R/2 is cut out of a solid sphere of radius R ...

    Text Solution

    |

  7. The range of parameter ' a ' for which the variable line y=2x+a lies b...

    Text Solution

    |

  8. A planet of mass m moves along an ellipse around the sun (mass M) so t...

    Text Solution

    |

  9. There are exactly two points on the ellipse x^2/a^2+y^2/b^2=1,whose di...

    Text Solution

    |

  10. The line2px+ysqrt(1-p^(2))=1(abs(p)lt1) for different values of p, tou...

    Text Solution

    |

  11. A point P moves such that the sum of the slopes of the normals drawn f...

    Text Solution

    |

  12. A rectangular hyperbola whose centre is C is cut by any circle of radi...

    Text Solution

    |

  13. Let P be a point on the hyperbola x^2-y^2=a^2, where a is a parameter,...

    Text Solution

    |

  14. Tangents are drawn from the points on a tangent of the hyperbola x^2-y...

    Text Solution

    |

  15. A tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 cuts the ellipse ...

    Text Solution

    |

  16. Let F(x) = (1+b^(2))x^(2) + 2bx + 1. The minimum value of F(x) is the ...

    Text Solution

    |