Home
Class 11
MATHS
Product of the perpendiculars from (alph...

Product of the perpendiculars from `(alpha, beta)` to the lines `ax^2+2hxy+by^2=0` is

A

`|aalpha^2-2halphabeta+b beta^2|/(sqrt({4h^2+(a+b)^2}))`

B

`|aalpha^2-2halphabeta+b beta^2|/(sqrt({4h^2-(a-b)^2}))`

C

`|aalpha^2-2halphabeta+b beta^2|/(sqrt({4h^2-(a+b)^2}))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos

Similar Questions

Explore conceptually related problems

prove that the product of the perpendiculars drawn from the point (x_1, y_1) to the pair of straight lines ax^2+2hxy+by^2=0 is |(ax_1^2+2hx_1y_1+by_1^2)/sqrt((a-b)^2+4h^2)|

The lines y = mx bisects the angle between the lines ax^(2) +2hxy +by^(2) = 0 if

If S_(1)=alpha^(2)+beta^(2)-a^(2) , then angle between the tangents from (alpha, beta) to the circle x^(2)+y^(2)=a^(2) , is

Find the values of the parameter a such that the rots alpha,beta of the equation 2x^2+6x+a=0 satisfy the inequality alpha//beta+beta//alpha<2.

A variable line passes through the fixed point (alpha,beta) . The locus of the foot of the perpendicular from the origin on the line is,

The gradient of one of the lines ax^2+2hxy+by^2=0 is twice that of the other, then

If the roots of the equation x^2-px+q=0 be alpha,beta and the roots of the equation x^2-ax+b=0 be alpha,1/beta then prove that, bq(a-p)^2=(q-b)^2 .

If the tangent to the curve 2y^3=ax^2+x^3 at the point (a,a) cuts off Intercepts alpha and beta on the coordinate axes, (where alpha^2+beta^2=61) then the value of a is

Two roots of the equation ax^2 +bx +c=0 is alpha,beta then find the value of alpha^2 + beta^2

PATHFINDER-CARTESIAN COORDINATES AND STRAIGHT LINE-QUESTION BANK
  1. The equation sqrt({(x-2)^2+y^2})+sqrt({(x+2)^2+y^2})=4 represents

    Text Solution

    |

  2. If the lines represented by x^2-2pxy-y^2=0 are rotated about the origi...

    Text Solution

    |

  3. Product of the perpendiculars from (alpha, beta) to the lines ax^2+2hx...

    Text Solution

    |

  4. The gradient of one of the lines ax^2+2hxy+by^2=0 is twice that of the...

    Text Solution

    |

  5. If pairs of straight lines x^2-2pxy-y^2=0and x^2-2qxy-y^2=0 be such th...

    Text Solution

    |

  6. If one of the pair of lines ax^2+2hxy+by^2=0 bisects the angle between...

    Text Solution

    |

  7. If the quadratic equation ax^2+bx+c=0 has -2 as one of its roots, then...

    Text Solution

    |

  8. The lines 2x-y-1=0, ax+3y-3=0 and 3x+2y-2=0 are concurrent for

    Text Solution

    |

  9. Given the family of lines, a(3x+4y+6) +b(x+y+2)=0. The line of the fam...

    Text Solution

    |

  10. If 3a+2b+6c=0, the family of straight lines ax+by+c=0 passes through a...

    Text Solution

    |

  11. Consider the family of lines (x+y-1)+lambda(2x+3y-5)=0 and (3x+2y-4)+m...

    Text Solution

    |

  12. P(3,1), Q(6,5) and R(x,y) are three points such that the angle PRQ is ...

    Text Solution

    |

  13. The area of the triangle having vertices (-2,1), (2,1) and (lim(mtoinf...

    Text Solution

    |

  14. If f(x+y)=f(x)f(y),forall x,y,inR and f(1)=2, then area enclosed by 3|...

    Text Solution

    |

  15. The difference of the tangents of the angles which the lines x^2(sec^2...

    Text Solution

    |

  16. Mixed term xy is to be removed from the general equation of second deg...

    Text Solution

    |

  17. Two of the straight lines given 3x^3+3x^2y-3xy^2+dy^3=0 are at right a...

    Text Solution

    |

  18. The vertices of a triangle are A(x1,x1tanalpha),(Bx2,x2tanbeta) and C(...

    Text Solution

    |

  19. If the distance of any point (x,y) from origin is defined as d(x,y)=ma...

    Text Solution

    |

  20. For all real values of a and b lines (2a+b)x + (a+3b)y+(b-3a)=0 and mx...

    Text Solution

    |