Home
Class 12
MATHS
For the equation ax^(2) +by^(2) + 2hxy...

For the equation
`ax^(2) +by^(2) + 2hxy + 2gx + 2fy + c =0` where `a ne 0`, to represent a circle, the condition will be

A

a=b and c=0

B

f=g and h=0

C

a=b and h=0

D

f=g and c=0

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|55 Videos

  • CIRCLES

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|12 Videos

  • CARTESIAN PRODUCT OF SETS AND RELATIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|31 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|59 Videos

Similar Questions

Explore conceptually related problems

the equation ax^(2)+ 2hxy + by^(2) + 2gx + 2 fy + c=0 represents an ellipse , if

IF the equation x^(2) + y^(2) + 2gx + 2fy + 1 = 0 represents a pair of lines, then

If the equation x^(2)+y^(2)+2hxy+2gx+2fy+c=0 represents a circle,then the condition for that circle to pass through three quadrants only but not passing through the origin is f^(2)>c (b) g^(2)>2c>0( d )h=0

The equation x^(2) + y^(2) + 2gx + 2fy + c = 0 represents a circle of non-zero radius , if

If the equation x^(2) + y^(2) + 2gx + 2fy + c = 0 represents a circle with X-axis as a diameter , and radius a, then :

Find the centre and radius of the circle ax^(2) + ay^(2) + 2gx + 2fy + c = 0 where a ne 0 .

The circle represented by the equation x ^(2) + y^(2) + 2gx + 2fy + c=0 will be a point circle, if

OBJECTIVE RD SHARMA-CIRCLES-Exercise
  1. If the circle x^2 + y^2 = a^2 cuts off a chord of length 2b from the l...

    Text Solution

    |

  2. The area of the circle centred at (1,2) and passing through (4,6) is

    Text Solution

    |

  3. For the equation ax^(2) +by^(2) + 2hxy + 2gx + 2fy + c =0 where a n...

    Text Solution

    |

  4. The equation of the circle passing through (4, 5) having the centre (2...

    Text Solution

    |

  5. Locus of centre of a circle of radius 2, which rolls on the outside of...

    Text Solution

    |

  6. Four distinct points (2k,3k) , (1,0), (0,1) and (0,0) lies on a circl...

    Text Solution

    |

  7. A square is inscribed in the circle x^2+y^2-2x+4y-93=0 with its sides ...

    Text Solution

    |

  8. A line is drawn through a fix point P(alpha, beta) to cut the circle x...

    Text Solution

    |

  9. The equation of circles passing through (3, -6) touching both the axes...

    Text Solution

    |

  10. The centre of a circle passing through the points (0, 0), (1, 0) and t...

    Text Solution

    |

  11. If 2x-4y=9 and 6x-12y+7=0 are parallel tangents to circle, then radiu...

    Text Solution

    |

  12. One of the diameters of the circle x^2+y^2-12x+4y+6=0 is given by

    Text Solution

    |

  13. The length of the chord cut off by y=2x+1 from the circle x^2+y^...

    Text Solution

    |

  14. Area of the circle in which a chord of lengthsqrt2 makes an angle pi/2...

    Text Solution

    |

  15. The coordinates of the middle point of the chord cut-off by 2x-5y+18=0...

    Text Solution

    |

  16. Find the equation of the circle which passes through the points (1,-2)...

    Text Solution

    |

  17. If the lines 3x-4y-7 = 0 and 2x-3y-5=0 are two diameters of a circle o...

    Text Solution

    |

  18. Equation of the circle with centre on the y-axis and passing through t...

    Text Solution

    |

  19. If the lines a1x+b1y+c1=0 and a2x+b2y+c2=0 cut the coordinae axes at c...

    Text Solution

    |

  20. If a circle passes through the points of intersection of the coordinat...

    Text Solution

    |