Home
Class 12
MATHS
Let (xr,yr),r=1,2,3,4 ne the points of i...

Let `(x_r,y_r),r`=1,2,3,4 ne the points of intersection the parabola "y^2=4ax" and the circle"x^2+y^2+2gx+2fy+c=0"prove that `y_1+y_2+y_3+y_4=0`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • Parabola

    A DAS GUPTA|Exercise EXERCISE|51 Videos

  • Pair of Straight Lines and Transformation of Axes

    A DAS GUPTA|Exercise EXERCISE|22 Videos

  • Product of three or more Vectors

    A DAS GUPTA|Exercise Exercise|28 Videos

Similar Questions

Explore conceptually related problems

If (x_(r),y_(r));r=1,2,3,4 be the points of intersection of the parabola y^(2)=4ax and the circle x^(2)+y^(2)+2gx+2fy+c=0, then

The points of intersection of the line 4x-3y-10=0 and the circle x^(2)+y^(2)-2x+4y-20=0 are

Find the point of intersection of the circle x^(2)+y^(2)-3x-4y+2=0 with the x -axis.

The equation of the normal at P(x_(1),y_(1)) to the circle x^(2)+y^(2)+2gx+2fy+c=0 is

Let A(x_(1), y_(1))" and "B(x_(2), y_(2)) be two points on the parabola y^(2)=4ax . If the circle with chord AB as a diameter touches the parabola, then |y_(1)-y_(2)|=

The tangent from the point of intersection of the lines 2x – 3y + 1 = 0 and 3x – 2y –1 = 0 to the circle x^(2) + y^(2) + 2x – 4y = 0 is

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

A DAS GUPTA-Parabola-EXERCISE
  1. Let (xr,yr),r=1,2,3,4 ne the points of intersection the parabola "y^2=...

    Text Solution

    |

  2. Find the equation of the parabola, if the focus is at (-6,-6) and the...

    Text Solution

    |

  3. Prove that the equation y^(2)+2ax+2by+c=0 represents a parabola whose ...

    Text Solution

    |

  4. Prove that the equation y^2-2y+8x-23=0reprsents a parabola and find it...

    Text Solution

    |

  5. If (a^2, a -2) be a point interior to the region of the parabola y^2...

    Text Solution

    |

  6. Show that the tangents at the extremities of any focal chord of a par...

    Text Solution

    |

  7. The orthocenter of a triangle formed by 3 tangents to a parabola y^2=4...

    Text Solution

    |

  8. Tangents are drawn from any point on the line x+4a=0 to the parabola y...

    Text Solution

    |

  9. Prove that the area of triangle formed by the tangents to the parabola...

    Text Solution

    |

  10. Points A, B, C lie on the parabola y^2=4ax The tangents to the parabol...

    Text Solution

    |

  11. If P, Q, R are three points on a parabola y^2=4ax whose ordinates are ...

    Text Solution

    |

  12. Prove that any three tangents to a parabola whose slopes are in harmon...

    Text Solution

    |

  13. Two straight lines are perpendicular to each other. One of them touche...

    Text Solution

    |

  14. Find the equation of the chord to the parabola y^2=4axwhose middle poi...

    Text Solution

    |

  15. Prove that the normal chord to a parabola at the point whose ordinate ...

    Text Solution

    |

  16. Show that the area formed by the normals to y^2=4ax at the points t1,t...

    Text Solution

    |

  17. P & Q are the points of contact of the tangents drawn from the point T...

    Text Solution

    |

  18. For what values of 'a' will the tangents drawn to the parabola y^2 = 4...

    Text Solution

    |

  19. Find the centre and radius of the smaller of the two circles that touc...

    Text Solution

    |

  20. Prove that the length of the intercept on the normal at the point P(a ...

    Text Solution

    |

  21. Prove that the locus of the middle pointsof chords of the parabolay^2=...

    Text Solution

    |