Home
Class 11
MATHS
If y(1),y(2),andy(3) are the ordinates o...

If `y_(1),y_(2),andy_(3)` are the ordinates of the vertices of a triangle inscribed in the parabola `y_(2)=4ax`, then its area is

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

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-

The slope of the tangent to the parabola y^(2)=4ax at the point (at^(2), 2at) is -

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

Show that the product of the ordinates of the ends of a focal chord of the parabola y^(2) = 4ax is constant .

The equation of the normal to the parabola y^(2) =4ax at the point (at^(2), 2at) is-

Length of the shortest normal chord of the parabola y^2=4ax is

Find the area of the equilateral triangle inscribed in the circle x^(2) + y^(2) - 4x + 6y - 3 = 0 .

Find the area bounded by the parabola y^(2) =4ax and its double ordinate x =b

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Let S be the focus of y^2=4x and a point P be moving on the curve s...

    Text Solution

    |

  2. If a!=0 and the line 2b x+3c y+4d=0 passes through the points of ...

    Text Solution

    |

  3. If y(1),y(2),andy(3) are the ordinates of the vertices of a triangle i...

    Text Solution

    |

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

    Text Solution

    |

  5. If P S Q is a focal chord of the parabola y^2=8x such that S P=6 , the...

    Text Solution

    |

  6. Parabolas y^(2)=4a(x-c(1))andx^(2)=4a(y-c(2)), where c(1) and c(2) are...

    Text Solution

    |

  7. A circle touches the x-axis and also touches the circle with centre (0...

    Text Solution

    |

  8. The locus of the vertex of the family of parabolas y=(a^(3)x^(2))/(3...

    Text Solution

    |

  9. Let C(1)andC(2) be, respectively, the parabola x^(2)=y-1andy^(2)=x-1. ...

    Text Solution

    |

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

    Text Solution

    |

  11. The locus of a point on the variable parabola y^2=4a x , whose distanc...

    Text Solution

    |

  12. Tangent to the curve y=x^2+6 at a point (1,7) touches the circle x^2+y...

    Text Solution

    |

  13. The angle between the tangents drawn from the point (1,4) to the para...

    Text Solution

    |

  14. Statement 1: There are no common tangents between the circle x^2+y^2...

    Text Solution

    |

  15. If the line x-1=0 is the directrix of the parabola y^2-k x+8=0 , then ...

    Text Solution

    |

  16. C (0,1) is the centre of the circle with radius unity. P is the parabo...

    Text Solution

    |

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

    Text Solution

    |

  18. The shortest distance between the parabolas 2y^2=2x-1 and 2x^2=2y-1 is...

    Text Solution

    |

  19. Normals at two points (x(1),y(1))and(x(2),y(2)) of the parabola y^(2)=...

    Text Solution

    |

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

    Text Solution

    |