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

`-2tanf`

B

`-2tan(p-f)`

C

0

D

`2cotf`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    MOTION|Exercise EXERCISE - III|25 Videos

  • PARABOLA

    MOTION|Exercise EXERCISE - IV|33 Videos

  • PARABOLA

    MOTION|Exercise EXERCISE - I|28 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 4 ( Level-II ) Previous Year (Paragraph)|2 Videos

  • PERMUTATION AND COMBINATION

    MOTION|Exercise EXAMPLE|23 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

MOTION-PARABOLA-EXERCISE - II
  1. If two tangents drawn from the point (a,b) to the parabola y^2=4x be...

    Text Solution

    |

  2. Find the equation of the common tangent to the curves y^2=8x and xy=-1...

    Text Solution

    |

  3. If the tangents and normals at the extremities of a focal chord of a ...

    Text Solution

    |

  4. The equation of a straight line passing through the point (3, 6) and c...

    Text Solution

    |

  5. T is a point on the tangent to a parabola y^(2) = 4ax at its point P. ...

    Text Solution

    |

  6. From the focus of parabola y^2 = 8x as centre, a circle is described s...

    Text Solution

    |

  7. The straight line joining any point P on the parabolay^2=4ax to the ve...

    Text Solution

    |

  8. The tangent and normal at P(t), for all real positive t, to the parabo...

    Text Solution

    |

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

    Text Solution

    |

  10. Two parabolas y(2) = 4a(x – 1l(1)) and x(2) = 4a(y – l(2)) always touc...

    Text Solution

    |

  11. Let A be the vertex and L the length of the latus rectum of the parabo...

    Text Solution

    |

  12. The parametric coordinates of any point on the parabola y^(2) = 4ax ca...

    Text Solution

    |

  13. The locus of the mid point of the focal radi of a variable point movin...

    Text Solution

    |

  14. Two parabolas have the same focus. If their directrices are the x-axis...

    Text Solution

    |

  15. The length of the chord of the parabola y^(2) = x which is bisected at...

    Text Solution

    |

  16. Tangent to the parabola y^(2) = 4ax at point P meets the tangents at v...

    Text Solution

    |

  17. A variable circle is described to passes through the point (1, 0) and ...

    Text Solution

    |