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two pair of straight lines have the equations y 2 +xy-12x 2 =0 and ax 2 +2hxy+by 2 =0.one line will be common among them if??

two pair of straight lines have the equations y2+xy-12x2=0 and ax2+2hxy+by2=0.one line will be common among them if??

Grade:12th pass

2 Answers

Gopal Gopakumar
27 Points
6 years ago
The equation of the given lines can be written as (y + 4x)(y – 3x) = 0
so the roots of y/x are either –4 or 3.
now rearranging the given equation,
 
b(y/x)2 + 2h(y/x) + a = 0
 
they will have a common line only if -4 or 3 is a root of the rearranged equation.
substituting values,
9b + 6h + a = 0    or 16b – 8h + a = 0
 
Thanks!
Shaik Asad
15 Points
4 years ago
Question - Two pairs of straight lines have eqns (1) and( 2)-[equations are given in solution]. One line will be common if ?
(A) a=-3(2h+3b)  (B)a=8(h-2b) (C) a=2(b+h)     (D)a=(b+h)
Y2+xy-12x2 =0 eq _  (1) and ax2+2hxy+by2 be eq-2)
Let y=mx be the common line for eq 1 and 2 and now substitute y value in both equations and take x2 common
we get (m2-m+12=0) -(3)Roots of eq (3)are +3 and
-4 substitute in eq 2 we get 9b+6h+a=0 eq-4
option (A) is correct if u want u can substitute value of a in eq 4
Thanks.. give me reply if it help u..
 

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