Home
Class 12
MATHS
The set of points on the axis of the par...

The set of points on the axis of the parabola `(x-1)^(2)=8(y+2)` from where three distinct normals can be drawn to the parabola is the set (h,k) of points satisfying

A

`hgt2`

B

`hgt1`

C

`kgt2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
(3) The axis of the parabola is x = 1. Any point on it is is (1,k).
Now, the distance of (1,k) from (1,-2) should be more than the semi-latus rectum, and (1,k) should be inside the parabola. Hence, `kgt2`.
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

From a point (d, 0) three normals are drawn to the parabola y^(2)=x , then

The set of points on the axis of the parabola y^2=4x+8 from which the three normals to the parabola are all real and different is (a) {(k ,0)"|"klt=-2} (b) {(k ,0)"|"kgt=-2} (c) {(0, k)"|"k gt=-2} (d) none of these

If three distinct normals to the parabola y^(2)-2y=4x-9 meet at point (h,k), then prove that hgt4 .

The point (8,4) lies inside the parabola y^(2) = 4ax If _

Find the equation of the normal to the parabola y^(2)=4ax at a point (x_(1),y_(1)) on it. Show that three normal can be drawn to a parabola from an external point.

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

Find the point where the line x+y=6 is a normal to the parabola y^2=8x .

If there exists at least one point on the circle x^(2)+y^(2)=a^(2) from which two perpendicular tangents can be drawn to parabola y^(2)=2x , then find the values of a.

Determine a point on the parabola x^(2)=8y which is nearest to the point (2,4).

If three normals are drawn from the point (c, 0) to the parabola y^(2)= x , then-

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

    |