Home
Class 12
MATHS
If the normals to the parabola y^2=4a x ...

If the normals to the parabola `y^2=4a x` at `P` meets the curve again at `Q` and if `P Q` and the normal at `Q` make angle `alpha` and`beta` , respectively, with the x-axis, then `t a nalpha(tanalpha+tanbeta)` has the value equal to

A

0

B

-2

C

`-1//2`

D

-1

Text Solution

Verified by Experts

The correct Answer is:
B
(2) `tanalpha=-t_(1)andtantanbeta=-t_(2)`
Also, `t_(2)=-t_(1)-(2)/(t_(1))`
`t_(1)t_(2)+t_(1)^(2)=-2`
`tanalphatanbeta+tan^(2)alpha=-2`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise EXERCISE (MULTIPLE CORRECT ANSWER TYPE )|26 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise LINKED COMPREHENSION TYPE|45 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.7|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

The normal to the parabola y^(2)=8x at the point (2, 4) meets the parabola again at the point-

If the normals to the parabola y^2=4a x at the ends of the latus rectum meet the parabola at Qa n dQ^(prime), then Q Q ' is

Prove that the normal at (am^(2),2am) to the parabola y^(2)=4ax meets the curve again at an angle tan^(-1)((1)/(2)m) .

A normal drawn to the parabola y^2=4a x meets the curve again at Q such that the angle subtended by P Q at the vertex is 90^0dot Then the coordinates of P can be

If a normal to a parabola y^2 =4ax makes an angle phi with its axis, then it will cut the curve again at an angle

If the normals at P, Q, R of the parabola y^2=4ax meet in O and S be its focus, then prove that .SP . SQ . SR = a . (SO)^2 .

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

If the normal chord of the parabola y^(2)=4x makes an angle 45^(@) with the axis of the parabola, then its length, is

Find the equation of normal to the parabola y^(2)=12x at (3t^(2),6t) . Hence, find the equation of the normal to this parabola which makes an angle 135^(@) with the x-axis.

If the line passing through the focus S of the parabola y=a x^2+b x+c meets the parabola at Pa n dQ and if S P=4 and S Q=6 , then find the value of adot

CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
  1. Evaluate, min[(x1-x2)^2+(5+sqrt(1-x1^2)-sqrt(4x2))^2],AAx1,x2 in R , ...

    Text Solution

    |

  2. If the normals to the parabola y^2=4a x at three points (a p^2,2a p), ...

    Text Solution

    |

  3. Normals A O ,A A1a n dA A2 are drawn to the parabola y^2=8x from the p...

    Text Solution

    |

  4. If the normals to the parabola y^2=4a x at the ends of the latus rectu...

    Text Solution

    |

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

    Text Solution

    |

  6. If the normals at P(t(1))andQ(t(2)) on the parabola meet on the same p...

    Text Solution

    |

  7. If the normals to the parabola y^2=4a x at P meets the curve again at ...

    Text Solution

    |

  8. PQ is a normal chord of the parabola y^2 =4ax at P, A being t...

    Text Solution

    |

  9. P ,Q , and R are the feet of the normals drawn to a parabola (y-3)^2=8...

    Text Solution

    |

  10. Normals at two points (x1y1)a n d(x2, y2) of the parabola y^2=4x meet ...

    Text Solution

    |

  11. The endpoints of two normal chords of a parabola are concyclic. Then ...

    Text Solution

    |

  12. If normal at point P on the parabola y^2=4a x ,(a >0), meets it again ...

    Text Solution

    |

  13. The set of points on the axis of the parabola (x-1)^(2)=8(y+2) from wh...

    Text Solution

    |

  14. Tangent and normal are drawn at the point P-=(16 ,16) of the parabola ...

    Text Solution

    |

  15. In parabola y^2=4x, From the point (15,12), three normals are drawn th...

    Text Solution

    |

  16. The line x-y=1 intersects the parabola y^2=4x at A and B . Normals at ...

    Text Solution

    |

  17. If normal are drawn from a point P(h , k) to the parabola y^2=4a x , t...

    Text Solution

    |

  18. The circle x^(2)+y^(2)+2lamdax=0,lamdainR, touches the parabola y^(2)=...

    Text Solution

    |

  19. The radius of the circle whose centre is (-4,0) and which cuts the par...

    Text Solution

    |

  20. If normal at point P on the parabola y^2=4a x ,(a >0), meets it again ...

    Text Solution

    |