Home
Class 11
MATHS
Prove that if the equation x^2+9y^2-4x+3...

Prove that if the equation `x^2+9y^2-4x+3=0` is satisfied for real values of `xa n dy ,t h e nx` must lie between 1 and 3 and`y` must lie between-1/3 and 1/3.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

If x^2 + 4y ^2 - 8x +12 =0 is satified by real values of x nad y then y must lies between

Find the real values of xa n dy , if (3x-7)+2i y=-5y+(5+x)i

The real number k for which the equation, 2x^3+""3x""+""k""=""0 has two distinct real roots in [0, 1] (1) lies between 2 and 3 (2) lies between -1 and 0 (3) does not exist (4) lies between 1 and 2

The real number k for which the equation, 2x^3+""3x""+""k""=""0 has two distinct real roots in [0, 1] (1) lies between 2 and 3 (2) lies between -1 and 0 (3) does not exist (4) lies between 1 and 2

Number of integral value (s) of k for which the equation 4x^(2)-16x+k=0 has one root lie between 1 and 2 and other root lies between 2 and 3, is

For what real values of k both the roots of equation x^2+2(k-3)x+9=-0 lie between -6 and 1.

If f(x , y) satisfies the equation 1+4x-x^2=sqrt(9sec^2y+4cos e c^2y) then find the value of xa n dtan^2ydot

Find the real values of x and y satisfying the equality (x-2 + (y-3)i)/(1+i)= 1-3t

If t is a real number satisfying the equation 2t^3-9t^2+30-a=0, then find the values of the parameter a for which the equation x+1/x=t gives six real and distinct values of x .

If x is real, prove that the value of the expression ((x-1)(x+3))/((x-2)(x+4)) cannot be between (4)/(9) and 1.

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find the domain and range of f(x)=sqrt(3-2x-x^2)

    Text Solution

    |

  2. If x in (0,pi//2)a n dcosx=1//3 , then prove that sum(n=0)^oo(cosn x)/...

    Text Solution

    |

  3. Prove that if the equation x^2+9y^2-4x+3=0 is satisfied for real value...

    Text Solution

    |

  4. Let Zp=rp(costhetap+isinthetap),p=1,2,3a n d1/(Z1)+1/(Z2)+1/(Z3)=0. Co...

    Text Solution

    |

  5. Find the least value of ((6x^2-22 x+21))/((5x^2-18x+17)) for real xdot

    Text Solution

    |

  6. Let a ,b and c be any three nonzero complex number. If |z|=1 and' z ' ...

    Text Solution

    |

  7. Find the range of the function f(x)=x^2-2x-4.

    Text Solution

    |

  8. If x=9^(1/3) 9^(1/9) 9^(1/27) ...->∞ , y= 4^(1/3) 4^(-1/9) 4^(1/27) ....

    Text Solution

    |

  9. Find the linear factors of 2x^2-y^2-x+x y+2y-1.

    Text Solution

    |

  10. If a<0,b>0, then sqrt(a)sqrt(b) is equal to (a)-sqrt(|a|b) (b...

    Text Solution

    |

  11. The value(s) of m for which the expression 2x^2+mxy+3y^2-5y-2 can be ...

    Text Solution

    |

  12. The number of solutions of z^2+overlinez = 0 is

    Text Solution

    |

  13. If a1x^3 + b1x² + c1x + d1 = 0 and a2x^3 + b2x^2+ c2x + d2 = 0 have a ...

    Text Solution

    |

  14. Consider the equation 10 z^2-3i z-k=0,w h e r ez is a following comple...

    Text Solution

    |

  15. If x-c is a factor of order m of the polynomial f(x) of degree n (1 < ...

    Text Solution

    |

  16. If z1a n dz2 are two complex numbers such that |z1|=|z2|a n d arg(z1)+...

    Text Solution

    |

  17. Solve the equation x^3-13 x^2+15 x+189=0 if one root exceeds the other...

    Text Solution

    |

  18. Let z1, z2, z3 be the three nonzero complex numbers such that z2!=1,a=...

    Text Solution

    |

  19. If tantheta and sectheta are the roots of a x^2+b x+c=0, then prove th...

    Text Solution

    |

  20. Given that the complex numbers which satisfy the equation | z bar z ^...

    Text Solution

    |