Home
Class 12
MATHS
If the equation ax^2 + 2hxy + by^2 + 2gx...

If the equation `ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0` represents a pair of parallel lines, prove that
`a/h = h/b = g/f`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise WBJEE Archive (2013)|17 Videos
  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise WBJEE Archive (2014)|5 Videos
  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise WBHS Archive (2016)|11 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion - Reason Type)|2 Videos
  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMINATION ( ASSERTION-REASON TYPE )|2 Videos

Similar Questions

Explore conceptually related problems

If the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 represents a pair of parallel lines, prove that The distance between them is 2sqrt((g^2 - ac)/(a(a + b)))

If the equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of parallel lines, prove that h=sqrt(ab) and gsqrtb=fsqrta or (h=-sqrt(ab)and gsqrtb=-fsqrta)

If the equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of parallel lines, then the distance between them is

The equation x^(2) + y^(2) + 2gx + 2fy + c = 0 represents a point-circle when -

If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 respresent the pair of parallel straight lines , then prove that h^(2)=abandabc+2fgh-af^(2)-bg^(2)-ch^(2)=0 .

9x^(2) +2hxy +4y^(2) +6x +2fy - 3 = 0 represents two parallel lines. Then

If the equation 2x^(2)+2hxy +6y^(2) - 4x +5y -6 = 0 represents a pair of straight lines, then the length of intercept on the x-axis cut by the lines is equal to

The equation x^2+y^2+2gx+2fy+c=0 represents a point -circle when

The equation a^2x^2+2h(a+b)x y+b^2y^2=0 and a x^2+2h x y+b y^2=0 represent

Under the conditions ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c = 0 will be the equation of a circle ? In that case what will be the coordinates of the centre ?

CHHAYA PUBLICATION-COORDINATE GEOMETRY-WBJEE Archive (2012)
  1. If the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 represents a pa...

    Text Solution

    |

  2. If the circles x^(2) + y^(2) + 2x + 2ky + 6 = 0 and x^(2) + y^(2) ...

    Text Solution

    |

  3. The line joining A (b cos alpha b sin alpha ) and B (a cos beta , ...

    Text Solution

    |

  4. If four distinct points (2k , 3k ) , (2 , 0) ,(0 , 3) and (0 , 0) lie ...

    Text Solution

    |

  5. Let the foci of the ellipse (x^(2))/(9) + y^(2) = 1 subtend a right ...

    Text Solution

    |

  6. Let P (2 , -3) , Q (-2 , 1) be the vertices of the triangle PQR . If t...

    Text Solution

    |

  7. Let P be the midpoint of a chord joining the vertex of the parabola...

    Text Solution

    |

  8. The line x =2 y intersects the ellipse (x^(2))/(4) +y^(2) = 1 at...

    Text Solution

    |

  9. The eccentric angle in the first quadrant of a point on the ellipse (x...

    Text Solution

    |

  10. The transverse axis of a hyperbola is along the x - axis and its leng...

    Text Solution

    |

  11. A point moves in such a way that the difference of its distances from...

    Text Solution

    |

  12. The number of integer values of m. for which the x - coordinate of the...

    Text Solution

    |

  13. If a straight line passes through the point (alpha , beta) and the...

    Text Solution

    |

  14. Let p , q , r be the altiudes of triangles with area s and perimeter ...

    Text Solution

    |

  15. Let C(1) and C(2) denote the centres of the circles x^(2) +y^(2)...

    Text Solution

    |

  16. A straight line through the point of intersection of the lines x + 2y ...

    Text Solution

    |

  17. Let P and Q be the points on the prabola y^(2) = 4x so that the lin...

    Text Solution

    |

  18. The incentre of an equilateral triangle is (1,1) and the equation of ...

    Text Solution

    |