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Analytical Geometry> two pair of straight lines have the equat...

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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??

alekhya , 9 Years ago

Grade 12th pass

2 Answers

Gopal Gopakumar

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!

Last Activity: 9 Years ago

Shaik Asad

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+by²be eq-2)

Let y=mx be the common line for eq 1 and 2 and now substitute y value in both equations and take x²common

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..

Last Activity: 7 Years ago

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