Home
Class 12
MATHS
From a point (sintheta,costheta), if thr...

From a point `(sintheta,costheta)`, if three normals can be drawn to the parabola `y^(2)=4ax` then the value of a is

A

(1/2,1)

B

[-1/2,0)

C

[1/2,1]

D

`(-1/2,0cup(0,12))`

Text Solution

Verified by Experts

The correct Answer is:
D
(4) Point `(sintheta,costheta)` lies on the circle `x^(2)+y^(2)=1" for "AAthetainR`.
Now, three normals can be drawn to the parabola `y^(2)=4ax` if `x=|2a|` meets this circle.
Hence, we must have
`costhetagt|2a|`
`or0lt|2a|lt1`
`or0|a|lt(1)/(2)`
`orain(-(1)/(2),0)cup(0,(1)/(2))`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Exercise (Multiple)|26 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise (Comprehension)|41 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise 5.7|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Question Bank|19 Videos

Similar Questions

Explore conceptually related problems

Three normals drawn from a point (hk) to parabola y^(2)=4ax

The number of normals drawn to the parabola y^(2)=4x from the point (1,0) is

From a point (h,k) three normals are drawn to the parabola y^2=4ax . Tangents are drawn to the parabola at the of the normals to form a triangle. The centroid G of triangle is

Three normals are drawn to the parabola y^(2) = 4x from the point (c,0). These normals are real and distinct when

Three normals drawn to the parabola y^(2) = 4x from the point (c, 0) are real and diferent if

If three distinct normals can be drawn to the parabola y^(2)-2y=4x-9 from the point (2a, 0) then range of values of a is

CENGAGE-PARABOLA-Exercise (Single)
  1. min[(x1-x^2)^2+(3+sqrt(1-x1 2)-sqrt(4x2))],AAx1,x2 in R , is 4sqrt(5)...

    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 ,AA1a n dAA2 are drawn to the parabola y^2=8x from the poi...

    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 the vertex ...

    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 to...

    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 parabola y^(2)=4ax,(agt0), meets it again at Q...

    Text Solution

    |