Home
Class 11
MATHS
If one of the lines given by the equatio...

If one of the lines given by the equation `a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)=0` coincides with one of the lines given by `a_(2)x^(2)+2h_(2)xy+b_(2)y^(2)=0` and the other lines represented by them are perpendecular then prove that.
`h_(1)((1)/(a_(1))-(1)/(b_(1)))=h_(2)((1)/(a_(2))-(1)/(b_(2)))`

Promotional Banner

Topper's Solved these Questions

  • PAIR OF STRAIGHT LINES

    AAKASH SERIES|Exercise EXERCISE -I|50 Videos

  • PAIR OF STRAIGHT LINES

    AAKASH SERIES|Exercise EXERCISE -II|105 Videos

  • PAIR OF STRAIGHT LINES

    AAKASH SERIES|Exercise EXERCISE - 4.3 ( LONG ANSWER QUESTIONS)|10 Videos

  • MULTIPLE PRODUCT OF VECTORS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|62 Videos

  • PERIODICITY AND EXTEME VALUES

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE) LEVEL-I(MAIN) Extreme values ( Single answer type questions )|23 Videos

Similar Questions

Explore conceptually related problems

If the slopes of the lines represented by 6x^(2)+2hxy+y^(2)=0 are in the ratio 1:2 then h=

The condition that one of the straight lines given by the equation ax^2+2hxy+by^2=0 " may coincide with one of those given by the equation " a'x^2+2h'xy+b' y^2=0 is

If the pair of lines a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)=0 and a_(2)x^(2)+2h_(2)xy+b_(3)y^(2)=0 have one line in common then show that (a_(1)b_(2)-a_(2)b_(1))^(2)+4(a_(1)h_(2)-a_(2)h_(1))(b_(1)h_(2)-b_(2)h_(1))=0

If slope of one of the lines represented by ax^(2)+2hxy+by^(2)=0 is n^(th) power of the other then prove that (ab^(n))^((1)/(n+1))+(a^(n)b)^((1)/(n+1))+2h=0

The pair of lines a^(2)x^(2)+2h(a+b)xy+b^(2)y^(2)=0 and ax^(2)+2hxy+by^(2)=0 are

One bisector of a(x-1)^(2)+2h(x-1)y+by^(2)=0 is 2x+y-2=0 is then other bisector is

One of the lines of -3x^(2)+2xy+y^(2)=0 is parallel to lx+y+1=0 then l=

If A,A_(1),A_(2),A_(3) are the areas of incircle and ex-circle of a triangle respectively then prove that (1)/(sqrt(A_(1)))+(1)/(sqrt(A_(2)))+(1)/(sqrt(A_(3)))=(1)/(sqrt(A))

If the equation (a_(1)-a_(2))x+(b_(1)-b_(2))y=c represents the perpendicular bisector of the segment joining (a_(1),b_(1)),(a_(2),b_(2)) then 2c=

If ax^(2) + by^(2) = 1, a_(1) x^(2) + b_(1)y^(2) = 1 , then show that the condition for orthogonality of above curves is (1)/(a)-(1)/(b)=(1)/(a_(1))-(1)/(b_(1))