Home
Class 12
MATHS
Area of the triangle formed by the verte...

Area of the triangle formed by the vertex, focus and one end of latusrectum of the parabola `(x+2)^(2)=-12(y-1)` is

A

36

B

18

C

9

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
(3) Consider equal parabola `y^(2)=12x`.
Vertex: V(0,0)
Focus: S(3,0)
End point of Lutus Rectum : A(3,6)
`:." Required area"=(1)/(2)SVxxAS=9` sq. units
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|4 Videos

Similar Questions

Explore conceptually related problems

The vertex of the parabola x^(2)=8y-1 is :

Find the vertex, focus, directrix, and length of the latus rectum of the parabola x^(2)-4x-5y-1=0

Find the vertex, focus and directrix of the parabola x^(2)=2(2x+y) .

The focus of the parabola x^2 -2x +8y + 17=0 is :

Square of the area of the triangle formed by end points of a focal chord P Q of length 32 units of the parabola y^2=8 x and its vertex is

Find the vertex of the parabola x^2=2(2x+y)

Find the area of the triangle formed by the lines joining the vertex of the parabola x^2 = 12y to the ends of its latus rectum.

Consider the parabola y^2 = 8x. Let Delta_1 be the area of the triangle formed by the end points of its latus rectum and the point P( 1/2 ,2) on the parabola and Delta_2 be the area of the triangle formed by drawing tangents at P and at the end points of latus rectum. Delta_1/Delta_2 is :

CENGAGE-PARABOLA-Exercise (Single)
  1. If X is the foot of the directrix on axis of the parabola. PP' is a d...

    Text Solution

    |

  2. A water jet from a function reaches it maximum height of 4 m at a d...

    Text Solution

    |

  3. Area of the triangle formed by the vertex, focus and one end of latusr...

    Text Solution

    |

  4. The locus of the vertices of the family of parabolas y =[a^3x^2]/3 + [...

    Text Solution

    |

  5. Two parabolas have the same focus. If their directrices are the x- and...

    Text Solution

    |

  6. The locus of the point (sqrt(3h),(sqrt(3)k+2)) if it lies on the line ...

    Text Solution

    |

  7. A circle touches the x-axis and also thouches the circle with center ...

    Text Solution

    |

  8. If parabolas y^2=lambdax and 25[(x-3)^2+(y+2)^2]=(3x-4y-2)^2 are equal...

    Text Solution

    |

  9. The length of the latus rectum of the parabola whose focus is ((u^2)/(...

    Text Solution

    |

  10. The graph of the curve x^2+y^2-2x y-8x-8y+32=0 falls wholly in the (a)...

    Text Solution

    |

  11. The vertex of the parabola whose parametric equation is x=t^2-t+1,y=t^...

    Text Solution

    |

  12. If the line y-sqrt(3)x+3=0 cut the parabola y^2=x+2 at P and Q , then ...

    Text Solution

    |

  13. A line is drawn form A(-2,0) to intersect the curve y^2=4x at Pa n dQ ...

    Text Solution

    |

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

    Text Solution

    |

  15. If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at Aa n dB , then th...

    Text Solution

    |

  16. If P is a point on the parabola y^2=3(2x-3) and M is the foot perpendi...

    Text Solution

    |

  17. A parabola y=a x^2+b x+c crosses the x-axis at (alpha,0) and (beta,0) ...

    Text Solution

    |

  18. The number of common chords of the parabolas x=y^2-6y+11 and y=x^2-6x+...

    Text Solution

    |

  19. Two parabolas have the same focus. If their directrices are the x- and...

    Text Solution

    |

  20. PSQ is a focal chord of a parabola whose focus is S and vertex is A. P...

    Text Solution

    |