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Mathematics
Mathematics
Problem
A circle touches a straight line
l
x
+
m
y
+
n
=
0
lx + my + n = 0
l
x
+
m
y
+
n
=
0
and cuts the circle
x
2
+
y
2
=
9
x^2 + y^2 = 9
x
2
+
y
2
=
9
orthogonally. The locus of centres of such circles is - (A)
(
l
x
+
m
y
+
n
)
2
=
(
l
2
+
m
2
)
(
x
2
+
y
2
−
9
)
(lx + my + n)^2 = (l^2 + m^2)(x^2 + y^2 - 9)
(
l
x
+
m
y
+
n
)
2
=
(
l
2
+
m
2
)
(
x
2
+
y
2
−
9
)
(C)
(
l
x
+
m
y
+
n
)
2
=
(
l
2
+
m
2
)
(
x
2
+
y
2
+
9
)
(lx + my + n)^2 = (l^2 + m^2)(x^2 + y^2 + 9)
(
l
x
+
m
y
+
n
)
2
=
(
l
2
+
m
2
)
(
x
2
+
y
2
+
9
)
(B)
(
l
x
+
m
y
−
n
)
2
=
(
l
2
+
m
2
)
(
x
2
+
y
2
−
9
)
(lx + my - n)^2 = (l^2 + m^2)(x^2 + y^2 - 9)
(
l
x
+
m
y
−
n
)
2
=
(
l
2
+
m
2
)
(
x
2
+
y
2
−
9
)
(D) none of these
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