Home
Class 12
MATHS
Given the equation 4x^2+2sqrt(3)x y+2y^2...

Given the equation `4x^2+2sqrt(3)x y+2y^2=1` . Through what angle should the axes be rotated so that the term `x y` is removed from the transformed equation.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|9 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CENGAGE ENGLISH|Exercise Comprehension Type|2 Videos

Similar Questions

Explore conceptually related problems

Though what angle should the axes be rotated so that the equation 9x^2 -2sqrt3xy+7y^2=10 may be changed to 3x^2 +5y^2=5 ?

Find the angle through which the axes be rotated to remove the xy term from the equation ax^(2)+2hxy+ay^(2) = 0

Find the transformed equation of 3x^(2)+10xy +3y^(2) = 9 when the axes are rotated through an angle pi/4

Find the transformed equation of x^(2)+2sqrt3 xy-y^(2) = 2a^(2) when the axes are rotated through an angle 30^(0).

Choose a new origin so that the equation 2x^(2)+7y^(2)+8x-14y+15 = 0 may be translated to the which the first degree terms be missing. Find the transformed equation also.

if the axes are rotated through 60 in the anticlockwise sense,find the transformed form of the equation x^2-y^2=a^2 ,

The transformed equation of x^(2)+6xy+8y^(2)=10 when the axes are rotated through an angled pi//4 is

If the transferred equation of a curve is x^(2) + 2sqrt(3)xy - y^(2) = 2a^(2) when the axes are rotated through an angle 60^(@) , then the original equation of the curve is

When the axes of rotated through 90^(0), find the transformed equation of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1

The transformed equation of x cos alpha + y sin alpha = p when the axes are rotated through an angle alpha is

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. If (2, 3, 5) is one end of a diameter of the sphere x^2+""y^2+""z^2...

    Text Solution

    |

  2. Convert r=4tanthetasectheta into its equivalent Cartesian equation.

    Text Solution

    |

  3. Given the equation 4x^2+2sqrt(3)x y+2y^2=1 . Through what angle should...

    Text Solution

    |

  4. The equation of a curve referred to a given system of axes is 3x^2+...

    Text Solution

    |

  5. Determine x so that the line passing through (3,4) and (x ,5) makes ...

    Text Solution

    |

  6. What does the equation 2x^2+4x y-5y^2+20 x-22 y-14=0 become when re...

    Text Solution

    |

  7. Shift the origin to a suitable point so that the equation y^2+4y+8x...

    Text Solution

    |

  8. At what point should the origin be shifted if the coordinates of a ...

    Text Solution

    |

  9. Find the equation to which the equation x^2+7x y-2y^2+17 x-26 y-60=0...

    Text Solution

    |

  10. The equation of curve referred to the new axes, axes retaining thei...

    Text Solution

    |

  11. If the point (2,3),(1,1), and (x ,3x) are collinear, then find the val...

    Text Solution

    |

  12. Which line is having the greatest inclination with the positive dire...

    Text Solution

    |

  13. Find the orthocentre of Delta A B C with vertices A(1,0),B(-2,1), ...

    Text Solution

    |

  14. The angle between the line joining the points (1,-2) , (3,2) and the l...

    Text Solution

    |

  15. The line joining the points A(2,1) and B(3,2) is perpendicular to the...

    Text Solution

    |

  16. For what value of k are the points (k ,2-2k)(-k+1,2k)a n d(-4-k ,6,6-2...

    Text Solution

    |

  17. Find the area of the quadrilateral A B C D having vertices A(1,1),B(...

    Text Solution

    |

  18. Given that P(3,1),Q(6. 5), and R(x , y) are three points such that t...

    Text Solution

    |

  19. If O is the origin and if the coordinates of any two points Q1 \ a n...

    Text Solution

    |

  20. Prove that the area of the triangle whose vertices are (t ,t-2),(t+...

    Text Solution

    |