. If a general equation of second degree 6x²_5xy + y²+ 5x – 2y + 1 = 0 is given Find the separate equations represented by above equation. [2] b. Find the point of intersection of these separate equations. Find the equation of bisectors of these separate equations of line. [2]
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Answer:
For a pair of straight lines given by the equationax
2
+2hxy+by
2
=0,equation of the angle bisectors is given by
a−b
x
2
−y
2
=
h
xy
Equation of the pair of straight lines is12x
2
−7xy−12y
2
=0
a=12,b=−12andh=
2
−7
∴Equation of the angle bisector is
24
x
2
−y
2
=
7
−2xy
or7x
2
+48xy−7y
2
=0
Equation of the pair of straight lines is71x
2
+94xy−71y
2
=0
a=71,b=−71andh=47
∴Equation of the angle bisector is
142
x
2
−y
2
=
47
xy
or47x
2
−142xy−47y
2
=0
Equation of the pair of straight lines isx
2
−y
2
=0
a=1,b=−1andh=0
∴Equation of the angle bisector is
2
x
2
−y
2
=
0
xy
orxy=0
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