Home
Class 12
MATHS
In parabola y^2=4x, From the point (15,1...

In parabola `y^2=4x`, From the point (15,12), three normals are drawn then centroid of triangle formed by three Co normal points is

A

A. `(16/3,0)`

B

B. `(4,0)`

C

C. `(26/3,0)`

D

D. `(6,0)`

Text Solution

Verified by Experts

The correct Answer is:
C
(3) Let the equation of any normal be `y=-tx+2t+t^(3)`.
Since it passes through the point (15,12) we have
`12=-15t+2t+t^(3)`
`ort^(3)-13t-12=0`
One root is -1. Then,
`(t+1)(t^(2)-t-12)=0`
`ort=-1,-3,4`
Therefore, the co-normal points are (1,-2), (9,-6), and (16,8).
Therefore, the centroid is (26/3,0).
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 centroid of the triangle formed by the points (1,2),(2,4)and (-3,6) is -

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.

If the normals from any point to the parabola y^2=4x cut the line x=2 at points whose ordinates are in AP, then prove that the slopes of tangents at the co-normal points are in GP.

How many normals can be drawn to parabola y^(2)=4x from point (15, 12)? Find their equation. Also, find corresponding feet of normals on the parabola.

y_(1) and y_(2) and y_(3) are the ordinates of three points on the parabola y ^(2) = 4ax, then the area of the triangle formed by the points is-

From the point (-1, -6) two tangents are drawn to the parabola y^(2)= 4x . Then the angle between the tangents is-

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

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

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

    |