Home
Class 11
MATHS
Statement 1: If the parabola y^2=4a x an...

Statement 1: If the parabola `y^2=4a x` and the circle `x^2+y^2+2b x=0` touch each other externally, then the roots of the equation `f(x)=x^2-(b+a+1)x+a=0` are real. Statement 2: For parabola and circle touching externally, `aa n db` must have the same sign.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

If the circles x^(2) +y^(2) = a and x^(2) + y^(2) - 6x - 8y + 9 = 0 touch externally then a =

Examine whether the two circles x^2+y^2-2x-4y=0 and x^2+y^2-8y-4=0 touch each other externally or internally .

If the circles x^(2) + y^(2) = k and x^(2) + y^(2) + 8x - 6y + 9 = 0 touch externally, then the value of k is

Prove that the curves y^2=4x and x^2+y^2-6x+1=0 touch each other at the points (1,\ 2) .

Prove that the curves y^2=4x and x^2+y^2-6x+1=0 touch each other at the points (1,\ 2) .

If the circles x^(2)+y^(2)=a^(2), x^(2)+y^(2)-6x-8y+9=0 touch externally then a=

If t_1a n dt_2 are the ends of a focal chord of the parabola y^2=4a x , then prove that the roots of the equation t_1x^2+a x+t_2=0 are real.

If t_1a n dt_2 are the ends of a focal chord of the parabola y^2=4a x , then prove that the roots of the equation t_1x^2+a x+t_2=0 are real.

Let y^2=4ax be a parabola and x^2+y^2+2bx=0 be a circle. If parabola and circle touch each externally then:

If the circle x^(2)+y^(2)+2ax=0, a in R touches the parabola y^(2)=4x , them

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Tangent is drawn at any point (x1, y1) other than the vertex on the pa...

    Text Solution

    |

  2. The angle between the tangents to the curve y=x^2-5x+6 at the point (2...

    Text Solution

    |

  3. Statement 1: If the parabola y^2=4a x and the circle x^2+y^2+2b x=0 to...

    Text Solution

    |

  4. If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at A and B , then th...

    Text Solution

    |

  5. P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) ...

    Text Solution

    |

  6. If a and c are the lengths of segments of any focal chord of the parab...

    Text Solution

    |

  7. AB is a chord of the parabola y^2 = 4ax with its vertex at A. BC is dr...

    Text Solution

    |

  8. The set of values of alpha for which the point (alpha,1) lies inside t...

    Text Solution

    |

  9. If P be a point on the parabola y^2=3(2x-3) and M is the foot of perpe...

    Text Solution

    |

  10. If y=m x+c touches the parabola y^2=4a(x+a), then (a)c=a/m (b) c=a m...

    Text Solution

    |

  11. The angle between the tangents to the parabola y^2=4a x at the points ...

    Text Solution

    |

  12. The area of the triangle formed by the tangent and the normal to the ...

    Text Solution

    |

  13. Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at...

    Text Solution

    |

  14. Statement 1: The normals at the points (4, 4) and (1/4,-1) of the para...

    Text Solution

    |

  15. The tangent PT and the normal PN to the parabola y^2=4ax at a point P...

    Text Solution

    |

  16. Let A and B be two distinct points on the parabola y^2=4x. If the ax...

    Text Solution

    |

  17. The equations of the common tangents to the parabola y = x^2 and y=-...

    Text Solution

    |

  18. about to only mathematics

    Text Solution

    |

  19. Let (x,y) be any point on the parabola y^2 = 4x. Let P be the point t...

    Text Solution

    |

  20. The common tangents to the circle x^2 + y^2 =2 and the parabola y^2 = ...

    Text Solution

    |