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Mathematics
Mathematics
Problem
If
x
2
−
y
2
+
2
h
x
y
+
2
g
x
+
2
f
y
+
c
=
0
x^2 - y^2 + 2hxy + 2gx + 2fy + c = 0
x
2
−
y
2
+
2
h
x
y
+
2
g
x
+
2
f
y
+
c
=
0
is the locus of a point, which moves such that it is always equidistant from the lines
x
+
2
y
+
7
=
0
x + 2y + 7 = 0
x
+
2
y
+
7
=
0
and
2
x
−
y
+
8
=
0
2x - y + 8 = 0
2
x
−
y
+
8
=
0
, then the value of
g
+
c
+
h
−
f
g + c + h - f
g
+
c
+
h
−
f
equals (2024 Main, 30 Jan II) (a) 29 (b) 14 (c) 8 (d) 6
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