Home
Class 12
MATHS
Line y=2x-b cuts the parabola y=x^(2)-4x...

Line y=2x-b cuts the parabola `y=x^(2)-4x` at points A and B. Then the value of b for which `angleAOB` is a right is (where O is origin) _________ .

Text Solution

Verified by Experts

The correct Answer is:
7
(7) The line is y=2x-b,i.e.,
`1=(2x-y)/(b)`
Homogenizing parabola with line, we get
`x^(2)-4x((2x-y)/(b))-y((2x-y)/(b))=0`
Since `angleAOB=90^(@)`
Coefficient of `x^(2)+"coefficient of "y^(2)=0`
`or1-(8)/(b)+(1)/(b)=0`
`orb=7`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE ENGLISH|Exercise ARCHIVES SINGLE CORRECT ANSWER TYPE|8 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise JEE ADVENCED SINGLE CORRECT ANSWER TYPE|2 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|5 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE ENGLISH|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE ENGLISH|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

A line from (-1,0) intersects the parabola x^(2)= 4y at A and B. Then the locus of centroid of DeltaOAB is (where O is origin) (a) 3x^(2) -2x =4y (b) 3y^(2) -2y = 4x (c) 3x^(2) +2x=4y (d) none of these

If the line x+y=6 is a normal to the parabola y^(2)=8x at point (a,b), then the value of a+b is ___________ .

if the line y=xsqrt3 cuts the curve x^3+y^3+3xy+5x^2+3y^2+4x+5y+1=0 at point A,B,C then find the value of OA.OB.OC is equal to (where O is the origin)

If y=mx+4 is common tangent to parabolas y^(2)=4x and x^(2)=2by . Then value of b is

If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at A and B , then the tangent of the angle subtended by line segment A B at the origin is (a) (8sqrt(3))/(205) (b) (8sqrt(3))/(209) (c) (8sqrt(3))/(215) (d) none of these

A variable line y=m x-1 cuts the lines x=2y and y=-2x at points Aa n dB . Prove that the locus of the centroid of triangle O A B(O being the origin) is a hyperbola passing through the origin.

If the line y-sqrt(3)x + 3=0 cuts the parabola y^2=x + 2 at A and B, then find the value of PA.PB(where P=(sqrt(3),0)

If the line y = x cuts the curve x^(3) + 3y^(3) - 30xy + 72x - 55 = 0 in points A,B and C, then the value of (4sqrt(2))/(55) OA.OB.OC (where O is the origin), is

y=3x is tangent to the parabola 2y=ax^2+b . The minimum value of a+b is

Two tangents to the circle x^2 +y^2=4 at the points A and B meet at P(-4,0) , The area of the quadrilateral PAOB , where O is the origin, is

CENGAGE ENGLISH-PARABOLA-NUMERICAL VALUE TYPE
  1. From the point (-1,2), tangent lines are to the parabola y^(2)=4x. If ...

    Text Solution

    |

  2. Line y=2x-b cuts the parabola y=x^(2)-4x at points A and B. Then the v...

    Text Solution

    |

  3. A line through the origin intersects the parabola 5y=2x^(2)-9x+10 at t...

    Text Solution

    |

  4. IF the circle (x-6)^2+y^2=r^2 and the parabola y^2=4x have maximum num...

    Text Solution

    |

  5. The slope of line which belongs to family (1+ l) x + (l-1)y + 2(1-l) =...

    Text Solution

    |

  6. If 3x+4y+k=0 represents the equation of tangent at the vertex of the ...

    Text Solution

    |

  7. Normals at (x(1),y(1)),(x(2),y(2))and(x(3),y(3)) to the parabola y^(2)...

    Text Solution

    |

  8. Foot of perpendicular from point P on the parabola y^(2)=4ax to the ax...

    Text Solution

    |

  9. about to only mathematics

    Text Solution

    |

  10. Normals are drawn from a point P with slopes m1,m2 and m3 are drawn fr...

    Text Solution

    |

  11. about to only mathematics

    Text Solution

    |

  12. about to only mathematics

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. ·If the normals of the parabola y^2=4x drawn at the end points of it...

    Text Solution

    |

  15. If the length of the latus rectum rectum of the parabola 169{(x-1)^(2)...

    Text Solution

    |

  16. If the line x+y=6 is a normal to the parabola y^(2)=8x at point (a,b),...

    Text Solution

    |

  17. Consider the locus of center of the circle which touches the circle x^...

    Text Solution

    |

  18. Line y=2x-b cuts the parabola y=x^(2)-4x at points A and B. Then the v...

    Text Solution

    |

  19. A line through the origin intersects the parabola 5y=2x^(2)-9x+10 at t...

    Text Solution

    |

  20. If 3x+4y+k=0 represents the equation of tangent at the vertex of the ...

    Text Solution

    |