Home
Class 12
MATHS
If X=x cos theta-y sin theta, Y=x sin t...

If `X=x cos theta-y sin theta, Y=x sin theta+y cos theta and X^(2)+4XY+Y^(2)=Ax^(2)+By^(2), 0 le theta le pi//2`, then :
(where A and B are constants)

A

`a=-1`, `b=3`

B

`theta=pi//4`

C

`a=3`, `b=-1`

D

`theta=(pi)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Topper's Solved these Questions

  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |5 Videos

  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise SELF PRACTIC PROBLEMS|25 Videos

Similar Questions

Explore conceptually related problems

If x = X cos theta- Y sin theta, y = X sin theta + Y cos theta and x^2 + 4 x y + y^2 = A X^2 + B Y^2 0 <= theta <= pi/2, then

If x/a cos theta + y/b sin theta = 1 , x/a sin theta - y/b cos theta = 1 then x^2/a^2 + y^2/b^2 =

If x =2 cos theta - cos 2 theta y = 2 sin theta - sin 2 theta Find (d^(2)y)/(dx^(2)) at theta = pi/2

If x +y= 3-cos4theta and x-y=4sin2theta then

Let x= cos theta and y = sin theta for any real value theta . Then x^(2)+y^(2)=

If x = 3 cos theta - 2 cos^3 theta,y = 3 sin theta - 2 sin^3 theta , then dy/dx is

Solve cos theta * cos 2 theta * cos 3 theta = (1)/( 4), 0 le theta le pi

if x = "cos" theta - "cos" 2 theta, y = "sin" theta - "sin" 2 theta , then dy/dx is

If x sin^3 theta+ y cos^3 theta = sin theta cos theta and x sin theta = y cos theta, Find the value of x^2 + y^2.

If x= a sin 2theta (1+ cos 2theta) , y= b cos 2theta(1- cos 2theta) , then (dy)/(dx) =

RESONANCE ENGLISH-FUNDAMENTAL OF MATHEMATICS-Exercise
  1. (1)/(sin3alpha)[sin^(3)alpha+sin^(3)((2pi)/(3)+alpha)+sin^(3)((4pi)/(3...

    Text Solution

    |

  2. (m+2)sin theta+(2m-1)cos theta=2m+1, if

    Text Solution

    |

  3. If X=x cos theta-y sin theta, Y=x sin theta+y cos theta and X^(2)+4XY...

    Text Solution

    |

  4. Prove that (1+tan1^0)(1+tan2^0)(1+tan45^0)=2^(23)dot

    Text Solution

    |

  5. Find the number of solutions to 2cosx=|sinx|,0lexle4pi.

    Text Solution

    |

  6. if the equation sin (pi x^2) - sin(pi x^2 + 2 pi x) = 0 is solved for ...

    Text Solution

    |

  7. In (0,6pi), the number of solutions of the equation tantheta+tan2theta...

    Text Solution

    |

  8. If 2tan^2x-5secx=1 for exactly seven distinct value of x in [0,(npi)/2...

    Text Solution

    |

  9. The number of integral values of a for which the equation cos2x+a sin ...

    Text Solution

    |

  10. If the arithmetic mean of the roots of the equation 4cos^(3)x-4cos^(2)...

    Text Solution

    |

  11. Number of solution of sinx cosx-3cosx+4sinx-13 gt 0 in [0,2pi] is equa...

    Text Solution

    |

  12. The solution of sqrt(5-2sinx) ge 6 sinx-1 is

    Text Solution

    |

  13. If (sin^(4)x)/(2)+(cos^(4)x)/(3)=1/5, then

    Text Solution

    |

  14. For 0 lt theta lt pi/2 , the solution (s) of sum(m=1)^6cos e c(theta+(...

    Text Solution

    |

  15. The maximum value of the expression 1/(sin^2theta+3sinthetacostheta+5c...

    Text Solution

    |

  16. The positive integer value of n gt 3 satisfying the equation (1)/(sin...

    Text Solution

    |

  17. The number of values of theta in the interval (-pi/2, pi/2) such that ...

    Text Solution

    |

  18. Let (x(0), y(0)) be the solution of the following equations: (2x)^("...

    Text Solution

    |

  19. about to only mathematics

    Text Solution

    |

  20. Let varphi,phi in [0,2pi] be such that 2costheta(1-sinphi)=sin^2theta(...

    Text Solution

    |