Home
Class 11
MATHS
If the pair of lines a(1)x^(2)+2h(1)xy+b...

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`

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • PAIR OF STRAIGHT LINES

    AAKASH SERIES|Exercise EXERCISE - 4.1 (VERY SHORT ANSWER QUESTIONS)|14 Videos

  • PAIR OF STRAIGHT LINES

    AAKASH SERIES|Exercise EXERCISE - 4.1 (SHORT ANSWER QUESTIONS)|14 Videos

  • PAIR OF STRAIGHT LINES

    AAKASH SERIES|Exercise SOLVED EXAMPLES|32 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

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

Theorem : A necessary and sufficient condition for the quadratic equations a_(1)x^(2)+b_(1)x+c_(1)=0" and "a_(2)x^(2)+b_(2)x+c_(2)=0 to have a common roots is (c_(1)a_(2)-c_(2)a_(1))^(2)=(a_(1)b_(2)-a_(2)b_(1))(b_(1)c_(2)-b_(2)c_(1))

If two circles x^(2)+y^(2)+2a_(1)x+2b_(1)y=0 and x^(2)+y^(2)+2a_(2)x+2b_(2)y=0 touches then show that a_(1)b_(2)=a_(2)b_(1)

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)))

If the lines a_(1)x+b_(1)y=1,a_(2)x+b_(2)y=1,a_(3)x+b_(3)y=1, are concurrent then the points (a_(1),b_(1)),(a_(2),b_(2)),(a_(3),b_(3))

If (a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)) are direction ratio of two lines such that (a_(1)^(2)+b_(1)^(2)+c_(1)^(2))(a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2))^(2)=0 then the two lines

If a_(1)Cos theta+b_(1) Sin theta+c_(1)=0 and a_(2) cos theta+ b_(2) sin theta +c_(2)= 0 then (b_(1)c_(2)-b_(2)c_(1))^(2)+(c_(1)a_(2)-c_(2)a_(1))^(2)=

The Cartesian equation of the sides BC,CA, AB of a triangle are respectively u_(1)=a_(1)x+b_(1)y+c_(1)=0, u_(2)=a_(2)x+b_(2)y+c_(2)=0 and u_(3)=a_(3)x+b_(3)y+c_(3)=0 . Show that the equation of the straight line through A bisectig the side bar(BC) is (u_(3))/(a_(3)b_(1)-a_(1)b_(3))=(u_(2))/(a_(1)b_(2)-a_(2)b_(1))

Show that two lines a_(1)x + b_(1) y+ c_(1) = 0 " and " a_(2)x + b_(2) y + c_(2) = 0 " where " b_(1) , b_(2) ne 0 are : (i) Parallel if a_(1)/b_(1) = a_(2)/b_(2) , and (ii) Perpendicular if a_(1) a_(2) + b_(1) b_(2) = 0 .

If sum_(r = 0)^(2n) a_(r ) (x-2)^(r ) = sum_(r = 0)^(2n) b_(r ) (x-3)^(r ) and a_(k ) =1 for all k ge n then show that b_(n ) =""^((2n+1)) C_((n+1)) .