Home
Class 12
MATHS
Consider two curves y^2 = 4a(x-lambda) a...

Consider two curves `y^2 = 4a(x-lambda)` and `x^(2)=4a(y-lambda)`, where `agt0` and `lambda` is a parameter. Show that
(i) there is a single positive value of `lambda` for which the two curves have exactly one point of intersection in the 1st quadrant find it.
(ii) there are infinitely many nagetive values of `lambda` for which the two curves have exactly one points of intersection in the 1st quadrant.
(iii) if `lambda=-a` , then find the area of the bounded by the two curves and the axes in the 1st quadrant.

Text Solution

Verified by Experts

The correct Answer is:
`=4/3(15+8sqrt(2))a^(2)`
Promotional Banner

Topper's Solved these Questions

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|10 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|20 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

Similar Questions

Explore conceptually related problems

The locus of the point x=a+lambda^(2),y=b-lambda where lambda is a parameter is

Prove that the family of curves x^2/(a^2+lambda)+y^2/(b^2+lambda)=1 , where lambda is a parameter, is self orthogonal.

If a circle passes through the points of intersection of the lines 2x-y +1=0 and x+lambda y -3=0 with the axes of reference then the value of lambda is :

If a circle passes through the points of intersection of the lines 2x-y+1=0 and x+lambda y-3=0 with the axes of reference then the value of lambda is

If a circle passes through the point of intersection of the lines x+y+1=0 and x+lambda y-3=0 with the coordinate axis,then value of lambda is

If x=(4 lambda)/(1+lambda^(2)) and y=(2-2 lambda^(2))/(1+lambda^(2)) where lambda is a real parameter and Z=x^(2)+y^(2)-xy then possible values of Z can be

If a circle passes through the points of intersection of the coordinate axes with the lines lambda x-y+1=0 and x-2y+3=0 then the value of lambda is.........

Find the range of values of lambda for which the point (lambda,-1) is exterior to both the parabolas y^(2)=|x|

The number of integral values of lambda for which exactly one root of the equation 5x^(2)+(lambda+1)x+lambda=0 lies in the interval (1,3) is

ARIHANT MATHS-AREA OF BOUNDED REGIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Consider two curves y^2 = 4a(x-lambda) and x^(2)=4a(y-lambda), where a...

    Text Solution

    |

  2. Area of region {(x,y) in R^(2): y ge sqrt(|x+3|,)5y le x + 9 le 15}

    Text Solution

    |

  3. Let F(x)=intx^[x^2+pi/6][2cos^2t.dt] for all x in R and f:[0,1/2] -> [...

    Text Solution

    |

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

    Text Solution

    |

  5. The area enclosed by the curvesy= sinx+cosx and y = | cosx-sin x | ove...

    Text Solution

    |

  6. Let S be the area of the region enclosed by y=e^-x^2,y=0,x=0,a n dx=1....

    Text Solution

    |

  7. Let f:[-1,2]vec[0,oo) be a continuous function such that f(x)=f(1-x)fo...

    Text Solution

    |

  8. Let the straight line x= b divide the area enclosed by y=(1-x)^(2),y=0...

    Text Solution

    |

  9. Area of the region bounded by the curve y=e^(x) and linesx=0 and y=e i...

    Text Solution

    |

  10. The area of the region bounded by the curves y=sqrt[[1+sinx]/cosx] and...

    Text Solution

    |

  11. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

    Text Solution

    |

  12. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

    Text Solution

    |

  13. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

    Text Solution

    |

  14. The area (in sqaure units) of the region {(x,y):x ge 0, x + y le 3, x^...

    Text Solution

    |

  15. The area (in sq units) of the region {(x, y) : y^2 gt= 2x and x^2 + y^...

    Text Solution

    |

  16. The area (in sq units) of the region described by {(x,y):y^(2)le2x and...

    Text Solution

    |

  17. The area (in sq. units) of the quadrilateral formed by the tangents...

    Text Solution

    |

  18. The area of the region described by A = {(x,y) : x^2 + y^2 lt= 1and y^...

    Text Solution

    |

  19. The area (in square units) bounded by the curves y=sqrt(x),2y-x+3=0, x...

    Text Solution

    |

  20. The area bounded between the parabola x^(2)=y/4 and x^(2)=9y and the s...

    Text Solution

    |

  21. The area of the region enclosed by the curves y=x, x=e,y=(1)/(x) and t...

    Text Solution

    |