What is the excess of the sum of 2x² + − y² + and x²+ 2y²− 5xy+ 3 over 4x² − 2xy + 3y?
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Answer:
1
2x
2
+5xy+3y
2
+7y+4=0
Comparing above eqn. with general eqn. of pair of straight line
ax
2
+2hxy+by
2
+2gx+2fy+c=0
We get a=2, h=
2
5
, b=3, g=0, f=
2
7
and c=4
Angle b/w pair of straight lines is
θ=tan
−1
[
a+b
2
h
2
−ab
]
tan
−1
m=tan
−1
⎣
⎢
⎢
⎢
⎡
2+3
2
4
25
−6
⎦
⎥
⎥
⎥
⎤
m =
5
25−24
m=
5
1
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