Home
Class 11
MATHS
The condition that one of the straight l...

The condition that one of the straight lines given by the equation `a x^2+2h x y+b y^2=0` may coincide with one of those given by the equation `a^(prime)x^2+2h^(prime)x y+b^(prime)y^2=0` is
`(a b^(prime)-a^(prime)b)^2=4(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h)` `(a b^(prime)-a^(prime)b)^2=(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h)` `(h a^(prime)-h^(prime)a)^2=4(a b^(prime)-a^(prime)b)(b h^(prime)-b^(prime)h)` `(b h^(prime)-b^(prime)h)^2=4(a b^(prime)-a^(prime)b)(h a^(prime)-h^(prime)a)`

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    CENGAGE PUBLICATION|Exercise All Questions|507 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|986 Videos

Similar Questions

Explore conceptually related problems

If (a x^2+b x+c)y+(a^(prime)x^2+b^(prime)x+c^(prime))=0 and x is a rational function of y , then prove that (a c^(prime)-a^(prime)c)^2=(a b^(prime)-a^(prime)b)xx(b c^(prime)-b^(prime)c)dot

The solution of the differential equation y^(prime)y^(primeprimeprime)=3(y^(primeprime))^2 is

If the equations x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0 have a common root, then it must be equal to a. (p^(prime)-p ^(prime) q)/(q-q^(prime)) b. (q-q ')/(p^(prime)-p) c. (p^(prime)-p)/(q-q^(prime)) d. (p q^(prime)-p^(prime) q)/(p-p^(prime))

If the circle x^2+y^2+2gx+2fy+c=0 bisects the circumference of the circle x^2+y^2+2g^(prime)x+2f^(prime)y+c^(prime)=0 then prove that 2g^(prime)(g-g^(prime))+2f^(prime)(f-f^(prime))=c-c '

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

If x^2+y^2=1, then (a) y y^('')-2(y^(prime))^2+1=0 (b) yy^('')+(y^(prime))^2+1=0 (c) y y^('')+(y^(prime))^(-2)-1=0 (d) y y^('')+2(y^(prime))^2+1=0

Find the condition if lines x=a y+b ,z=c y+da n dx=a^(prime)y+b^(prime), z=c^(prime)y+d ' are perpendicular.

If f(x)=xsinx, then find f^(prime)(pi/2)

The general solution of the differential equation, y^(prime)+yphi^(prime)(x)-phi(x)phi^(prime)(x)=0 , where phi(x) is a known function, is

If g(x)=int_(sinx)^("sin"(2x))sin^(-1)(t)dt ,t h e n : (a) g^(prime)(pi/2)=-2pi (b) g^(prime)(-pi/2)=-2pi (c) g^(prime)(-pi/2)=2pi (d) g^(prime)(pi/2)=2pi

CENGAGE PUBLICATION-STRAIGHT LINES-All Questions
  1. The straight lines represented by (y-mx)^(2)=a^(2)(1+m^(2))and(y-nx)^(...

    Text Solution

    |

  2. If the pairs of lines x^(2)+2xy+ay^(2)=0andax^(2)+2xy+y^(2)=0 have e...

    Text Solution

    |

  3. The condition that one of the straight lines given by the equation a x...

    Text Solution

    |

  4. If the lines represented by the equation 3y^2-x^2+2sqrt(3)x-3=0 are ro...

    Text Solution

    |

  5. A point moves so that the distance between the foot of perpendicula...

    Text Solution

    |

  6. The angle between the pair of lines whose equation is 4x^(2)+10xy+my^...

    Text Solution

    |

  7. Find the point of intersection of the pair of straight lines represent...

    Text Solution

    |

  8. Find the angle between the lines represented by x^(2)+2xysectheta+y^(2...

    Text Solution

    |

  9. If the pair of lines sqrt(3)x^(2)-4xy+sqrt(3)y^(2)=0 is rotated about...

    Text Solution

    |

  10. If the equation 2x^(2)+kxy+2y^(2)=0 represents a pair of real and dist...

    Text Solution

    |

  11. If the equation x^2+(lambda+mu)x y+lambdau y^2+x+muy=0 represents two ...

    Text Solution

    |

  12. If one of the lines of the pair a x^2+2h x y+b y^2=0 bisects the angle...

    Text Solution

    |

  13. Prove that the equation 2x^(2)+5xy+3y^(2)+6x+7y+4=0 respresents a pai...

    Text Solution

    |

  14. A line L passing through the point (2, 1) intersects the curve 4x^2+y^...

    Text Solution

    |

  15. Show that straight lines (A^2-3B^2)x^2+8A Bx y+(B^2-3A^2)y^2=0 form wi...

    Text Solution

    |

  16. If one of the lines denoted by the line pair a x^2+2h x y+b y^2=0 bise...

    Text Solution

    |

  17. If the middle points of the sides BC, CA, and AB of triangle ABC are (...

    Text Solution

    |

  18. Find the equations of the lines which pass through the origin and are ...

    Text Solution

    |

  19. If (-2,6) is the image of the point (4,2) with respect to line L=0, th...

    Text Solution

    |

  20. If the lines x+(a-1)y+1=0 and 2x+a^2y-1=0 are perpendicular, then find...

    Text Solution

    |