Home
Class 11
MATHS
The parabola y=x^2+p x+q cuts the straig...

The parabola `y=x^2+p x+q` cuts the straight line `y=2x-3` at a point with abscissa 1. Then the value of `pa n dq` for which the distance between the vertex of the parabola and the x-axis is the minimum is (a) `p=-1,q=-1` (b) `p=-2,q=0` (c) `p=0,q=-2` (d) `p=3/2,q=-1/2`

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

If the straight line y= 4x -5 touches the curve y^(2) = px^(3) + q at (2, 3), then the values of p and q are-

IF p^3-q(3p-1)+q^2=0 , find the relation between the roots of the equation x^2+px+q=0 .

If the circles x^2+y^2+2a x+c y+a=0 and x^2+y^2-3a x+d y-1=0 intersects at points P and Q , then find the values of a for which the line 5x+b y-a=0 passes through Pa n dQdot

If length of focal chord P Q is l , and p is the perpendicular distance of P Q from the vertex of the parabola, then prove that lprop1/(p^2)dot

If the difference of the roots of the equation x^2-px+q=0 is 1, then show that p^2+4q^2= (1+2q)^2 .

If normal at point P on the parabola y^2=4a x ,(a >0), meets it again at Q in such a way that O Q is of minimum length, where O is the vertex of parabola, then O P Q is

Let P be the point (1,0) and Q a point on the parabola y^(2) =8x, then the locus of mid-point of bar(PQ is-

The line P Q whose equation is x-y=2 cuts the x-axis at P ,a n dQ is (4,2). The line P Q is rotated about P through 45^0 in the anticlockwise direction. The equation of the line P Q in the new position is

If the line y=3x+c touches the parabola y^2=12 x at point P , then find the equation of the tangent at point Q where P Q is a focal chord.

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

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. If normal at point P on the parabola y^2=4a x ,(a >0), meets it again ...

    Text Solution

    |

  2. If line P Q , where equation is y=2x+k , is a normal to the parabola w...

    Text Solution

    |

  3. The parabola y=x^2+p x+q cuts the straight line y=2x-3 at a point with...

    Text Solution

    |

  4. Tangent is drawn at any point (p ,q) on the parabola y^2=4a xdot Tange...

    Text Solution

    |

  5. The equation of the directrix of the parabola with vertex at the origi...

    Text Solution

    |

  6. Tangent is drawn at any point (x1, y1) other than the vertex on the pa...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. AB is a chord the parabola y^(2)=4ax with vertex A. BC is drawn perpen...

    Text Solution

    |

  13. Set of value of alpha for which the point (alpha,1) lies inside the ci...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. The angle between the tangents to the paranola y^(2)=4ax at the points...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Let A and B two distinct points on the parabola y^(2)=4x. If the axis ...

    Text Solution

    |