Home
Class 12
MATHS
A(cos t , sin t), B(sin t ,-cos t) and C...

`A(cos t , sin t), B(sin t ,-cos t) and C(a,b)` form an equilateral triangle , `t in [0,2pi]` and orthocentre of this triangle lies on a circle with centre `(1,1/3)` then `a^2-b^2` is equal to

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN 2021

    JEE MAINS PREVIOUS YEAR|Exercise Mathematic section B|10 Videos

  • JEE MAIN 2023

    JEE MAINS PREVIOUS YEAR|Exercise Question|435 Videos

Similar Questions

Explore conceptually related problems

x=a cos t, y=b sin t

If sin t+cos t=(1)/(5) then tan((t)/(2)) is equal to:

If x=A cos 4t+B sin4t, then (d^(2)x)/(dt^(2)) is equal to

If vertices of a triangle ABC are A(1,2),B(3,4) and C(-5,3) and its orthocentre is O, then reflecton of orthocentre of triangle OBC w.r.t.line y=x will be (a,b) then a+b is equal to

If x=e^t sin t , y=e^t cos t , t is a parameter , then (d^2y)/(dx^2) at (1,1) is equal to

If sin theta=(2t)/(1+t^(2)) and theta lies in 2 nd quadrant then cos theta is equal to

x=3sin t-2 sin ^3t, y=3 cos t -2cos^3t

JEE MAINS PREVIOUS YEAR-JEE MAIN 2022-Question
  1. Tangent at two points P and Q on parabola y^2=2x-3 meet at R(0,1) , th...

    Text Solution

    |

  2. Let hyperbola H : x^2-y^2=1 and ellipse E : x^2/a^2+y^2/b^2=1 and ecce...

    Text Solution

    |

  3. A(cos t , sin t), B(sin t ,-cos t) and C(a,b) form an equilateral tria...

    Text Solution

    |

  4. A password is to be made of 6 to 8 digits from either of the sets A,B,...

    Text Solution

    |

  5. The solution of differential equation sin^2(2x) dy/dx+(8sin^2(2x)+4 si...

    Text Solution

    |

  6. Let f(x)=(5x^2)/2 +alpha/x^5, (x gt 0) and minimum value of f(x) is 14...

    Text Solution

    |

  7. If (p^(**)q) odot (p odot ~q) is tautology then ordered pair (odot ,^(...

    Text Solution

    |

  8. Let x^2+y^2-x+2y=11/4 is a circle with RQ and centre C. If P is any po...

    Text Solution

    |

  9. Let A relation R on number defined by xRy hArr 3x+alpha y is multiple ...

    Text Solution

    |

  10. The value of 15 int0^sqrt3 (xdx)/(sqrt(1+x^2+sqrt((1+x^2)^3))) is equa...

    Text Solution

    |

  11. If P(B//A)=5/7 , P(A//B)=7/9 and P(AnnB)=1/9 given S1 equiv P(A' uu B)...

    Text Solution

    |

  12. Absolute maximum value of f(x)=tan^(-1)(sinx-cosx) is

    Text Solution

    |

  13. A class have B boys and G girls , 3 boys and 2 girls selected at rando...

    Text Solution

    |

  14. The number of distinct real values of lamda for which (x-1)/1=(y-2)/2=...

    Text Solution

    |

  15. If tangent drawn from (2,0) to the parabola x=-2y^2 are also tangents ...

    Text Solution

    |

  16. Let f(x)=lim(x to oo)(cos 2pi x -x^(2n) sin (x-1))/(1+x^(2n+1)-x^(2n))...

    Text Solution

    |

  17. Let f(x)=ax^2+bx+c and f(1)=3 , f(-2)=lamda , f(3)=4 then value of lam...

    Text Solution

    |

  18. The value of 60 int0^(pi/2) (sin 6x)/(sinx) dx is

    Text Solution

    |

  19. If 1+(2+^49C1+^49C2+. . .+^49C49)("^50C2+^50C4+^50C6+. . .+^50C50)=m.2...

    Text Solution

    |

  20. The differential equation of all the circles passing through the point...

    Text Solution

    |