Home
Class 12
MATHS
Let f (x,y)= x^(2) - y^(2) and g (x,y)=2...

Let `f (x,y)= x^(2) - y^(2) and g (x,y)=2xy.` such that `(f ( x,y))^(2) -(g (x,y))^(2)=1/2 and f (x,y) . G(x,y) =(sqrt3)/(4)` Find the number of ordered pairs `(x,y) ` ?

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    VIKAS GUPTA (BLACK BOOK)|Exercise MATCHING TYPE PROBLEMS|1 Videos
  • ELLIPSE

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-4 : Subjective Type Problems|2 Videos
  • HYPERBOLA

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-4 : Subjective Type Problems|3 Videos

Similar Questions

Explore conceptually related problems

If f(x+y,x -y)= xy then (f(x,y)+f(y,x))/(2)=

Let f(x,y)=x^(2)+2xy+3y^(2)-6x-2y, where x, y in R, then

If f(x,y)=2x^(2)-xy+2y^(2) then find f_x at the point (1,2)

If f(x,y)=2x^(2)-xy+2y^(2) then find f_x at the point (1,2)

Let f :R to R be a continous and differentiable function such that f (x+y ) =f (x). F(y)AA x, y, f(x) ne 0 and f (0 )=1 and f '(0) =2. Let f (xy) =g (x). G (y) AA x, y and g'(1)=2.g (1) ne =0 The number of values of x, where f (x) g(x):

If f (x, y) = 2x ^ (3) -11x ^ (2) y + 3y ^ (3), show that: x (delta f) / (delta x) + y (delta f) / (delta y ) = 3f (x, y)

VIKAS GUPTA (BLACK BOOK)-FUNCTION -SUBJECTIVE TYPE PROBLEMS
  1. For the real number x, let f (x)=(1)/( ""^(2011sqrt(1-x^(2011)))). Fi...

    Text Solution

    |

  2. Find the number of elements contained in the range of the function f (...

    Text Solution

    |

  3. Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -...

    Text Solution

    |

  4. Let f (x) = (x+5)/(sqrt(x^(2) +1) ) , then the smallest integral va...

    Text Solution

    |

  5. The number of integral values of m for which f : R to R ,f (x) = (x ^(...

    Text Solution

    |

  6. The number of roots of equation ((x-1)(x-3))/((x-2)(x-4))-e^(x)) ((x+1...

    Text Solution

    |

  7. Let f(x)=x^2-bx+c,b is an odd positive integer. Given that f(x)=0 ha...

    Text Solution

    |

  8. Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x...

    Text Solution

    |

  9. If f (x) = 4x ^(3) -x ^(2) -2x +1 and g (x) = {{:(min {f(t): 0 le t le...

    Text Solution

    |

  10. If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...

    Text Solution

    |

  11. Let f x = (ax+b)/(xa+d), where a,b,c d are non zero If f (7) =7,f (11)...

    Text Solution

    |

  12. Let A = {x|x ^(2) -4x+ 3 lt 0 , x in R} B={x|2^(1-x)+p le 0;x^2-2(p+7...

    Text Solution

    |

  13. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |

  14. If f(x) is an even function then find the number of distinct real numb...

    Text Solution

    |

  15. The least integral value of m, m inR for which the range of function ...

    Text Solution

    |

  16. Let x1, x2, x3 satisfying the equation x^3 - x^2 + betax + gamma = 0 ...

    Text Solution

    |

  17. The value of sum(r=1)^1024 [log2 r] is equal to, ([.] denotes the gre...

    Text Solution

    |

  18. Let f (x) = (ax+b)/(cx+d), where a,b,c d are non zero If f (7) =7,f (1...

    Text Solution

    |

  19. It is pouring down rain and the amount of rain hitting point (x,y) is ...

    Text Solution

    |

  20. Let P (x) be a cubic polynomical with leading co-efficient unity. Let ...

    Text Solution

    |