Home
Class 11
MATHS
Tangent is drawn at any point (p ,q) on ...

Tangent is drawn at any point `(p ,q)` on the parabola `y^2=4a xdot` 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`

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

Tangent is drawn at any point (x_1, y_1) other than the vertex on the parabola y^2=4a x . If tangents are drawn from any point on this tangent to the circle x^2+y^2=a^2 such that all the chords of contact pass through a fixed point (x_2,y_2), then

The tangent at any point P onthe parabola y^2=4a x intersects the y-axis at Qdot Then tangent to the circumcircle of triangle P Q S(S is the focus) at Q is

T P and T Q are tangents to the parabola y^2=4a x at Pa n dQ , respectively. If the chord P Q passes through the fixed point (-a ,b), then find the locus of Tdot

The common tangents to the circle x^(2)+y^(2)=2 and the parabola y^(2)=8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQSR is

P,Q and R three points on the parabola y^(2)=4ax . If Pq passes through the focus and PR is perpendicular to the axis of the parabola, show that the locus of the mid point of QR is y^(2)=2a(x+a) .

Find the points of contact Q and R of a tangent from the point P(2,3) on the parabola y^2=4xdot

If PQ and Rs are normal chords of the parabola y^(2) = 8x and the points P,Q,R,S are concyclic, then

The tangents to the parabola y^2=4a x at the vertex V and any point P meet at Q . If S is the focus, then prove that S PdotS Q , and S V are in GP.

The common tangents to the circle x^2 + y^2 =2 and the parabola y^2 = 8x touch the circle at P,Q andthe parabola at R,S . Then area of quadrilateral PQRS is

If P S Q is a focal chord of the parabola y^2=8x such that S P=6 , then the length of S Q is

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. If line P Q , where equation is y=2x+k , is a normal to the parabola w...

    Text Solution

    |

  2. The parabola y=x^2+p x+q cuts the straight line y=2x-3 at a point with...

    Text Solution

    |

  3. Tangent is drawn at any point (p ,q) on the parabola y^2=4a xdot Tange...

    Text Solution

    |

  4. The equation of the directrix of the parabola with vertex at the origi...

    Text Solution

    |

  5. Tangent is drawn at any point (x1, y1) other than the vertex on the pa...

    Text Solution

    |

  6. The angle between the tangents to the curve y=x^2-5x+6 at the point (2...

    Text Solution

    |

  7. Statement 1: If the parabola y^2=4a x and the circle x^2+y^2+2b x=0 to...

    Text Solution

    |

  8. If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at A and B , then th...

    Text Solution

    |

  9. P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) ...

    Text Solution

    |

  10. If a and c are the lengths of segments of any focal chord of the parab...

    Text Solution

    |

  11. AB is a chord the parabola y^(2)=4ax with vertex A. BC is drawn perpen...

    Text Solution

    |

  12. Set of value of alpha for which the point (alpha,1) lies inside the ci...

    Text Solution

    |

  13. If P is a point on the parabola y^(2)=3(2x-3) and M is the foot perpen...

    Text Solution

    |

  14. If y=m x+c touches the parabola y^2=4a(x+a), then (a)c=a/m (b) c=a m...

    Text Solution

    |

  15. The angle between the tangents to the paranola y^(2)=4ax at the points...

    Text Solution

    |

  16. The area of the triangle formed by the tangent and the normal to the ...

    Text Solution

    |

  17. Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at...

    Text Solution

    |

  18. Statement 1: The normals at the points (4, 4) and (1/4,-1) of the para...

    Text Solution

    |

  19. Let A and B two distinct points on the parabola y^(2)=4x. If the axis ...

    Text Solution

    |

  20. The equations of the common tangents to the parabola y = x^2 and y=-...

    Text Solution

    |