Home
Class 12
MATHS
Through the vertex O of the parabola y^2...

Through the vertex `O` of the parabola `y^2=4a x` , two chords `O Pa n dO Q` are drawn and the circles on OP and OQ as diameters intersect at `Rdot` If `theta_1,theta_2` , and `varphi` are the angles made with the axis by the tangents at `P` and `Q` on the parabola and by `O R ,` then value of `cottheta_1+cottheta_2` is `-2tanvarphi` (b) `-2tan(pi-varphi)` 0 (d) `2cotvarphi`

A

`-2tan phi`

B

`2tanphi`

C

0

D

`2cot phi`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|24 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise For Session 2|25 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|28 Videos

Similar Questions

Explore conceptually related problems

Through the vertex O of the parabola y^(2)=4ax, variable chords O Pand OQ are drawn at right angles.If the variables chord PQ intersects the axis of x at R, then distance OR

Through the vertex O of the parabola y^(2) = 4ax , a perpendicular is drawn to any tangent meeting it at P and the parabola at Q. Then OP, 2a and OQ are in

Through the vertex O of a parabola y^(2) = 4x chords OP and OQ are drawn at right angles to one another. Show that for all position of P, PQ cuts the axis of the parabola at a fixed point.

Through the vertex A of the parabola ((z-bar(z))/(2i))^(2)=2(z+bar(z)), where z=x+i y , (i=sqrt(-1)) two chords AP and AQ are drawn and the circles on AP and AQ as diameters intersect in R . If m_(1) , m_(2), m_(3) are slopes of tangent to parabola at P ,tangent to parabola at Q , AR respectively then find |(1)/(m_(1)m_(3))+(1)/(m_(2)m_(3))|

Through the vertex 'O' of parabola y^(2)=4x chords OP and OQ are drawn at right angles to one another.Show that for all positions of P, PQ cuts the axis of the parabola at a fixixed point.Also find the locus of the middle point of PQ.

If theta is the angle between the tangents to the parabola y^(2)=12x passing through the point (-1,2) then |tan theta| is equal to

If Q1 and Q2 are the angles made by tangents to the axis of parabola y^(2)=4x from the point P. If Q_(1)+Q_(2)=45^(@) then locus of P is

ARIHANT MATHS-PARABOLA-Exercise (Single Option Correct Type Questions)
  1. If the normals to the parabola y^2=4a x at P meets the curve again at ...

    Text Solution

    |

  2. If the normals at P, Q, R of the parabola y^2=4ax meet in O and S be...

    Text Solution

    |

  3. Length of the shortest normal chord of the parabola y^2=4ax is

    Text Solution

    |

  4. The largest value of a for which the circle x^2 +y^2 = a^2 falls total...

    Text Solution

    |

  5. From a point (sintheta,costheta), if three normals can be drawn to the...

    Text Solution

    |

  6. If two different tangents of y^2=4x are the normals to x^2=4b y , then

    Text Solution

    |

  7. The shortest distance between the parabolas 2y^2=2x-1 and 2x^2=2y-1 is...

    Text Solution

    |

  8. Normals at two points (x1,x2) and (x2,y2) of the parabola y^2=4x meet ...

    Text Solution

    |

  9. A line is drawn from A(-2,0) to intersect the curve y^2 = 4x in P and ...

    Text Solution

    |

  10. An equilateral triangle SAB in inscribed in the parabola y^2 = 4ax hav...

    Text Solution

    |

  11. C is the centre of the circle with centre (0,1) and radius unity. y=ax...

    Text Solution

    |

  12. Let S be the focus of y^2=4x and a point P be moving on the curve such...

    Text Solution

    |

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

    Text Solution

    |

  14. Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixe...

    Text Solution

    |

  15. Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q...

    Text Solution

    |

  16. A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to...

    Text Solution

    |

  17. If the fourth term in the expansion of (px+1/x)^n is 5/2, then (n,p)...

    Text Solution

    |

  18. The set of points on the axis of the parabola y^2-4x-2y+5=0 from which...

    Text Solution

    |

  19. The tangent to the parabola y=x^2 has been drawn so that the abscissa ...

    Text Solution

    |

  20. if y=4x+3 is parallel to a tangent to the parabola y^2=12x, then its d...

    Text Solution

    |