Home
Class 12
MATHS
The equation of a curve referred to a gi...

The equation of a curve referred to a given system of axes is `3x^2+2x y+3y^2=10.` Find its equation if the axes are rotated through an angle `45^0` , the origin remaining unchanged.

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

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

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

If the transformed equation of a curve is 17x^(2) - 16xy + 17y^(2)=225 when the axes are rotated through an angle 45^(@) , then the original equation of the curve is

If the transformed equation of a curve is 17x^(2) - 16xy + 17y^(2)=225 when the axes are rotated through an angle 45^(@) , then the original equation of the curve is

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

The transformed equation of 3x^(2)+3y^(2)+2xy-2=0 when the coordinats axes are rotated through an angle of 45^(@) , is

The equation of curve referred to the new axes, axes retaining their directions, and origin (4,5) is X^2+Y^2=36 . Find the equation referred to the original axes.

The equation of curve referred to the new axes, axes retaining their directions, and origin (4,5) is X^2+Y^2=36 . Find the equation referred to the original axes.

Find the equation of the lines through the point (3, 2) which make an angle of 45 with the line x-2y=3 .

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Convert r=4tanthetasectheta into its equivalent Cartesian equation.

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Find the area of a triangle having vertices A(3,2),B(11,8) and C(8,12)...

    Text Solution

    |