Home
Class 11
MATHS
Prove that the area of the traingle insc...

Prove that the area of the traingle inscribed in the parabola `y^2=4ax` is `1/(8a)(y_1~y_2)(y_2~y_3)(y_3~y_1)`, where `y_1,y_2,y_3` are the ordinates of the vertices.

Promotional Banner

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    CBSE COMPLEMENTARY MATERIAL|Exercise section(C) (Short Answer Type Question) (4 Marks)|17 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CBSE COMPLEMENTARY MATERIAL|Exercise Short Answer Type Questions|49 Videos

  • INTRODUCTION TO THREE-DIMENSIONAL COORDINATE GEOMETRY

    CBSE COMPLEMENTARY MATERIAL|Exercise SHORT ANSWER TYPE QUESTIONS|20 Videos

Similar Questions

Explore conceptually related problems

If the tangents to the parabola y^(2)=4ax at (x_(1),y_(1)),(x_(2),y_(2)) intersect at (x_(3),y_(3)) then

If the tangents to the parabola y^(2)=4ax at (x_1,y_1) and (x_2,y_2) meet on the axis then x_1y_1+x_2y_2=

If the tangents to the parabola y^2=4ax at the points (x_1,y_1) and ( (x_2,y_2) meet at the point (x_3,y_3) then

If y_(1),y_(2),y_(3) be the ordinates of a vertices of the triangle inscribed in a parabola y^(2)=4ax then show that the area of the triangle is (1)/(8a)|(y_(1)-y_(2))(y_(2)-y_(3))(y_(3)-y_(1))|

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

Show that the equation of the chord of the parabola y^2 = 4ax through the points (x_1, y_1) and (x_2, y_2) on it is : (y-y_1) (y-y_2) = y^2 - 4ax

If (x_1,y_1),(x_2,y_2)" and "(x_3,y_3) are the feet of the three normals drawn from a point to the parabola y^2=4ax , then (x_1-x_2)/(y_3)+(x_2-x_3)/(y_1)+(x_3-x_1)/(y_2) is equal to

If a parabola y^(2)=4ax followed by x_(1)x_(2)=a^(2),y_(1)y_(2)=-4a^(2) then (x_(1),y_(1)),(x_(2),y_(2)) are

The coordinates of the ends of a focal chord of the parabola y^(2)=4ax are (x_(1),y_(1)) and (x_(2),y_(2)). Then find the value of x_(1)x_(2)+y_(1)y_(2)

Equilateral traingles are circumscribed to the parabola y^2=4ax . Prove that their angular points lie on the conic (3x+a)(x+3a)=y^2

CBSE COMPLEMENTARY MATERIAL-COORDINATE GEOMETRY-section(D) (Long Answer Type Questions ) (6 Marks)
  1. A circle has radius 3u n i t s and its centre lies on the line y=x-1. ...

    Text Solution

    |

  2. find the equation of the circle which passes through the points (20,3)...

    Text Solution

    |

  3. Find the equation of the circle having (1,-2) as its centre and passin...

    Text Solution

    |

  4. Prove that the equation y^2+2Ax+2By+c=0 is represent a parabola and wh...

    Text Solution

    |

  5. Show that the points A(5,5), B(6,4), C(-2,4) and D(7,1) all lies on t...

    Text Solution

    |

  6. Find the equation of the ellipse whose minor aixs is equal to the dist...

    Text Solution

    |

  7. Find the equation of the hyperbola whose axes (transverse and conjugat...

    Text Solution

    |

  8. prove that the line 3x+4y+7=0 touches the circle x^2+y^2-4x-6y-12=0 al...

    Text Solution

    |

  9. The equation of the ellipse whose focus is (1,0) and the directr...

    Text Solution

    |

  10. Prove that the area of the traingle inscribed in the parabola y^2=4ax ...

    Text Solution

    |

  11. The equation of the tangent to the circle x^(2)+y^(2)-2x-4y-4=0 which ...

    Text Solution

    |

  12. find the equations of tangents to the circle x^2+y^2-4x-6y-12=0 which ...

    Text Solution

    |

  13. Find the equation of the parabola whose focus is (1,-1) and whose vert...

    Text Solution

    |

  14. Find the equation of the hyperbola whose directrix is 2x+y=1, focus(1,...

    Text Solution

    |

  15. find the equation of cicle in the following case touches both the ...

    Text Solution

    |

  16. find the equation of circle in each of the following cases ...

    Text Solution

    |

  17. find the equation of cicle in each of the following cases ) (c)touche...

    Text Solution

    |

  18. find the equation of cicle in each of the following cases )(d) touche...

    Text Solution

    |

  19. Find the equation of a circle which touches x-axis at the origin and w...

    Text Solution

    |

  20. find the equation of cicle in each of the following cases ) (f)touche...

    Text Solution

    |