Grade 12th passAnalytical Geometry
Given one equation about pair of lines like aX2+Y2+4X+3Y=0 FIND VALUE OF a
Given one equation about pair of lines like aX2+Y2+4X+3Y=0 FIND VALUE OF a
1 Answer
Vikas TU
Dear Student,
The general equation of a pair of straight lines is ax2+2hxy+by2+2gx+2fy+c=0.
The condition that this represents a pair of straight lines is (hy – af)2 = (h2 – ab)(g2 – ac).
In this equation, we have ax2+y2+4x+3y=0.
Therefore we have h=0, b=1, g=2, f=3/2, c=0.
Substituting this in the equation, we get (- 3a/2)2 = (0 – a)(4 – 0) = - 4a.
Therefore 9a2/4 = - 4a.
a = 0 or a = - 16/9.
The general equation of a pair of straight lines is ax2+2hxy+by2+2gx+2fy+c=0.
The condition that this represents a pair of straight lines is (hy – af)2 = (h2 – ab)(g2 – ac).
In this equation, we have ax2+y2+4x+3y=0.
Therefore we have h=0, b=1, g=2, f=3/2, c=0.
Substituting this in the equation, we get (- 3a/2)2 = (0 – a)(4 – 0) = - 4a.
Therefore 9a2/4 = - 4a.
a = 0 or a = - 16/9.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)
Thapar University)
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